It opens at the Dursleys' home where Harry Potter (Daniel Radcliffe) lives and is staying, as usual, during the summer holidays. Uncle Vernon's (Richard Griffiths) sister Marge (Pam Ferris) comes to visit and treats Harry with general contempt. She viciously insults him and his parents, angering Harry who unwittingly uses his innate magical powers to cause her to inflate, and float off, out of the Dursleys' house and into the twilight. Harry flees the Dursleys' home, furious. At first he walks with determination but soon grinds to a stop as he realizes he hasn't anywhere to go. He sits down at the edge of the road with his trunk. His surroundings stir as the wind picks up and a street lamp flickers above him. A jet black dog emerges from the bushes opposite, growling at him and he raises his wand. At that instant however, the eccentric Knight Bus, for lost witches or wizards, makes a sharp appearance and escorts Harry on a wacky journey to the wizards' pub 'The Leaky Cauldron.' While there, Harry learns that Sirius Black (Gary Oldman), an alleged supporter of Lord Voldemort, the dark wizard, has escaped from Azkaban prison. Harry must meet the Minister of Magic Cornelius Fudge (Robert Hardy) and he fears expulsion from Hogwarts for his using of under-age magic out of school. However, the matter is surprisingly dropped as "...the Ministry doesn't send students to Azkaban for blowing up their aunts." While at The Leaky Cauldron Harry also reconvenes with his two best friends, Ron Weasley (Rupert Grint) and Hermione Granger (Emma Watson), and the rest of the Weasley family. Mr. Arthur Weasley (Mark Williams) pulls Harry to one side to warn him about Sirius Black. He suggests that Harry needs to be cautious of Sirius Black due to his allegiance with Voldemort. He believes that Harry is the only thing which stands in the way of Voldemort returning to power and that it is on this premise that Sirius Black has escaped from Azkaban. To find and kill Harry Potter.
Harry, Ron and Hermione board the train to Hogwarts, discovering in their compartment the sleeping Professor Remus Lupin (David Thewlis) who is to be the new 'Defence Against the Dark Arts' teacher. Harry airs his concerns about Black's escape and his possible objective to Ron and Hermione. Tension builds during their discussion however as the train is stopped on a bridge and the lights pop out in each cabin. Ron peers out of the window, concerned that "...there is something out there." The train is violently jolted and a great cold descends around them, ice creeping over the windows. In the corridor outside, a scary dark creature slowly appears, floating towards them. It opens the door to their cabin and begins to engage frighteningly with Harry, sucking at his whole body. The sleeping teacher suddenly wakes, stands up, and repels the creature with a very bright white light emanating from his wand. Harry faints. On his coming round Lupin gives him chocolate to eat and explains that the creature is a 'Dementor' which drains happiness from anything it approaches. The Dementors ordinarily guard the wizard prison, 'The Prison of Azkaban' but are out searching for the escapee Black, and entered the train looking for him. Harry heard a woman screaming during the ordeal, but no one else heard it.
As Harry begins his third year at Hogwarts we learn of some significant changes. Alongside the official announcement of the formerly encountered, new Defence Against the Dark Arts teacher, Professor Lupin. Rubeus Hagrid (Robbie Coltrane), the groundsman, becomes additionally a professor of 'Care of Magical Creatures.' Also, Hermione seems to be taking nearly twice as many classes as everyone else, including some which are taught simultaneously.
During a Divination class, Professor Trelawney (Emma Thompson) foresees Harry's death in the tealeaves of his cup, which form the shape of a 'Grim' or large dog. In tealeaf reading this symbolises death. In Hagrid's first class, Draco Malfoy (Tom Felton) deliberately provokes Buckbeak, a Hippogriff, into attacking and injuring him. Draco's father, Lucius Malfoy, a powerful Ministry of Magic member of staff, files an official complaint. In Defence Against the Dark Arts, Professor Lupin instructs the class in the defeat of a Boggart, which changes its form to appear as one's greatest fear. When Harry steps up, it manifests itself as a Dementor, however Lupin steps in to defeat it before Harry gets the chance.
Harry is told he can't go on the school outings to Hogsmeade, a local village inhabited solely by magical beings, as he hasn't got his admission slip signed, and watches his friends go without him. Instead, he meets with Lupin, and Harry discovers that the reason he wasn't allowed to fight the Boggart was that Lupin had been worried it would take the shape of Voldemort. This concern catches Harry by surprise, because Harry had been thinking even more fearfully about the Dementors. Later that night, Sirius Black breaks into Hogwarts and destroys the Fat Lady's (Dawn French) portrait that guards Gryffindor Tower. The students spend the night sleeping in the Great Hall while the teachers search the castle for Black. Because Black is believed at large in the castle Dementors are sent specifically to patrol the perimeter of Hogwarts. Next day, Professor Snape (Alan Rickman) replaces Lupin as Defence Against the Dark Arts teacher while Lupin is intriguingly "...incapable of teaching at the present time." In an odd divergence from routine, he teaches the class about Werewolves.
During the next school Quidditch match, a popular wizard sport, several Dementors approach and try to engage their powers over Harry, causing him to faint and fall off his broomstick. Dumbledore (Michael Gabon) breaks Harry's fall, but his broomstick flies off into the magical tree, the 'Whomping Willow' and is destroyed. Dumbledore is angry that the Dementors came within school grounds as they are prohibited from doing so. Harry wonders why the Dementors seem to have a special interest in him and Lupin reveals that this is due to the horrors within Harry's past. Harry considers that he needs to know how to defend himself against them and convinces Lupin as such, who agrees to teach him.
At the time of the next school outing, still keen to go to Hogsmeade, Harry attempts to sneak into the village under his Invisibility Cloak, but is caught by Fred and George Weasley (James and Oliver Phelps), who give him the Marauder's Map. It is a map of the entire school and shows the real-time locations of everyone on the grounds. Fred and George also tell Harry that the map shows the whereabouts of several secret passages out of Hogwarts, ideal for leaving undetected. Once in Hogsmeade village, and back under his Invisibility Cloak, Harry catches sight of the Minister Fudge and Professor Minerva McGonagall (Maggie Smith) chatting in the street, discussing Black and himself. He follows them as they go inside and is shocked to overhear that Sirius Black was his parents' best friend and is still his godfather and a legal guardian. Black supposedly divulged the Potter's secret whereabouts to Lord Voldemort and murdered their friend Peter Pettigrew, as well as twelve Muggle bystanders (non-magic humans). Harry vows to kill Black. On returning from the outing we find out from Hagrid that as a consequence of Lucuis Malfoy's complaint, Buckbeak has been sentenced to death. That same night, after hours, Harry is astonished when he sees the aforementioned Peter Pettigrew's name on the Marauder's Map. He goes looking for him but can't find him. After Professor Snape discovers Harry out of bed, the map is confiscated by Lupin who meets them, and, covering for Harry, tells Snape it is merely a joke parchment and of no significance.
Harry has the agreed private class with Lupin, in which he must generate a Patronus, a shield that is used to repel the Dementors. Lupin has him test himself out on a Boggart. He fails the first time, but conjures one on his second attempt. Later on, returning to a recently finished Divinations class to bring back a crystal ball knocked over by Hermione, Harry reencounters Professor Trelawney. She grabs Harry by the shoulder, speaks as though possessed, and predicts that "...the Dark Lord's servant will return to him that night and that innocent blood shall be spilled."
When Harry, Ron and Hermione learn that Buckbeak is to be executed, they visit Hagrid in his hut to console him. On the way Draco taunts them about it and Hermione punches him in the face. While there, Hagrid says they cannot remain with him during the execution and that Buckbeak can't be set free, since the officials would know it was Hagrid. Hagrid has also found Ron's lost rat Scabbers, and returns him to Ron. Ron had wrongly believed that his rat had been eaten by Hermione's cat. As the execution party approaches the hut, stones fly in through the window and they leave and run back to the edge of the castle, watching the execution from afar. Scabbers then bites Ron, who chases after him, finally collecting him under the Whomping Willow. The black dog makes another appearance and attacks Ron and drags him, along with Scabbers, into a hole at the tree's base. Harry and Hermione follow, finding a tunnel which leads them to the Shrieking Shack.
Inside, in a fast moving scene, Harry finally confronts Sirius Black who he has been led to believe wishes to kill him, and whom he wishes to kill. We discover that as an illegal Animagus, Black can transform into animal at will, thus he is also the infamous black dog. Professor Lupin, who had spotted the group on the confiscated Marauder's Map, suddenly bursts in and embraces his old friend Black. Confronted by Hermione, Lupin admits to being a werewolf. Lupin and Black then explain that Black is not the one who betrayed the Potters, rather it was Peter Pettigrew (Timothy Spall), who has been hiding for twelve years in his Animagus form as Scabbers, Ron's rat. He is Voldemort's servant, not Black, and he framed Black for his crimes. Meanwhile Snape bursts in also confronting Black but is disposed of by Harry. Harry is skeptical of the story until Black and Lupin force Pettigrew back into his human form, and after some squealing resistance Pettigrew finally confesses that it is true, proving Black's innocence. Black further clears up the misunderstanding by explaining, that on discovering Pettigrew was still alive, he escaped Azkaban in order to kill him. As Lupin and Black are about to kill Pettigrew, Harry stops them, and showing Pettigrew mercy, tells him they will take him back to the castle, where he can be left for the Dementors.
As the group heads back to the castle, Harry and Sirius pause and chat optimistically. Harry remarks that Pettigrew would have been of no use dead. Firstly he didn't want his father's two best friends to be killers, and secondly he is the key in proving Sirius's innocence. Sirius suggests Harry comes to live with him. They are disturbed however, when, as the full moon rises, it causes Lupin to turn into the dangerous werewolf since he had neglected to take his potion which inhibits this transformation. Black responds by transforming again into the black dog in order to protect Harry, Ron and Hermione. The werewolf and Black have a vicious fight. During the ensuing commotion, Pettigrew transforms himself back into the rat and escapes, not pursued. Harry runs forward in his angst at Sirius's torture at the hands of the werewolf, inadvertently attracting its attention. However while approaching Harry, it is distracted by some other distant werewolf cry. Meanwhile, Sirius, badly injured, has moved down to the nearby lake where he lies at the edge. Harry follows and kneels over him. As he does so, a swarm of Dementors approaches them. Harry produces a Patronus to try and fend them off, however it is not nearly strong enough and they both begin to submit to the Dementors. Then on the other side of the river appears the brilliant white symbol of a stag and an immense Patronus which drives the Dementors away. Harry faints.
Harry awakens in the hospital wing to hear the news, that Sirius Black has been captured and is about to be given the Dementor's Kiss, to suck out his soul. Dumbledore enters and Harry, Ron and Hermione try and convince him of Black's innocence. Dumbledore somehow already knows, but says that their word alone won't be believed. However, he suggests mysteriously, that Harry and Hermione travel in time back by using Hermione's time-turning device (we now find out how she has been attending simultaneous classes), and at least save both Black and Buckbeak from their fates. Hermione turns her hour-glass necklace back three turns (three hours), and Harry and Hermione are together thrust into the past, where they observe and remould the evenings events. They throw stones through the window of Hagrid's hut, alerting themselves of the approaching execution party. They rescue Buckbeak while the execution party is inside with Hagrid shortly before the execution, thus absolving Hagrid of any blame. Hermione diverts the attention of the werewolf Lupin stalking the past Harry with an imitation of another werewolf's cry. And, from a hiding place in the forest, Harry watches the Dementor sequence and realizes, as the stag symbol fails to appear, that he must have been the one who conjured the powerful Patronus. After saving his past self and Black from the Dementors, Harry and Hermione fly on Buckbeak's back to the tower, where Black is imprisoned, and rescue him. Harry and Black share a moment of contemplation, as since Black is going to be back on the run, still wanted and without proof of his innocence, their relationship will now be sadly fraught with complications and Harry's dream of living with his godfather is shattered. However, Harry takes comfort in knowing that Black, although still considered a fugitive, is at least free and safe for the time being. Black and Buckbeak leave, Black riding on his back. Harry and Hermione make it back to the hospital wing just as the timeline restores itself, and a reticent Dumbledore merrily bids them goodnight.
As the school year end approaches, Lupin announces that he is resigning, believing that parents of the students would not be comfortable in the now open knowledge that he is a werewolf. He returns the Marauder's Map to Harry since he is no longer a professor. Harry later receives a gift from an unknown source, a Firebolt, an extremely fast racing broom. Hermione holds up a large feather, also contained within the parcel, confirming that Sirius must have sent it. Harry tries it out and is whisked away from sight, ending the film with the snapshot image of Harry flying his new broom, ecstatic.