Over the opening credits a large set of a woman's lips in red lipstick sing the opening song ('Science Fiction-Double Feature').
Brad Majors (Barry Bostwick) and Janet Weiss (Susan Sarandon) are two "normal, ordinary, healthy kids" in November 1974 from the small town of Denton, Ohio whom they first meet in Dr. Scott's college refresher course and fell in love. Now as the movie opens, they are attending the wedding of Ralph Hapschatt (Jeremy Newson) and Betty Monroe (Hilary Labow) in which Brad is Ralph's best man and Janet is the maid of honor. Inspired by the events around him, as soon as the other guests leave, Brad asks Janet to marry him in a song ('Damnit Janet') inside the church and she accepts. Joyous, the couple decide to go tell Dr. Scott the good news.
Appearing all through the movie, a Criminologist (Charles Gray) comes on and explains that we are about to embark on a strange journey following the misadventures of Brad and Janet. He mentions that despite the storm clouds gathering, the two decided to go for a long drive in the country anyway even though their spare tire was badly in need of air. He claims that Brad and Janet will have "a night to remember for a very long, time."
Back to Brad and Janet, as they drive on, the sun sets and, sure enough, it begins to rain very heavily. Janet is starting to feel ill at ease considering how far out they are and that a bunch of bikers keep passing them on the road and suggests that they should turn back before something bad happens. We hear a loud BANG! and the car skids to a stop.
Brad realizes he messed up badly by not refilling the spare tire and suggests that the two of them go to an old castle they passed along the way to call for help. Janet isn't so sure this is a good idea, but Brad talks her into it anyway as there's not much they can do otherwise. As they walk through the rain, Janet tries to shield herself with a newspaper, telling herself through a song that no matter how bad things get, there's always a good side and that things will always get better. ('There's a Light... over at the Frankenstein Place')
Soon the two arrive on the front doorstep of the castle. Brad knocks and just as the two were about to leave, the door is opened by Riffraff (Richard O'Brien), a tall, gaunt, balding butler in a stark black suit. He glares at them, further unnerving Janet, though Brad tries to be friendly, introducing himself and Janet and explaining that they need a phone as their car has broken down nearby.
The foyer is outlandishly decorated with dark wooden furniture, stuffed dead animals and hunting trophies, and random relics and curiosities. Riffraff explains to Brad and Janet that they've arrived on a very special night as "the master" is having a party, where Brad and Janet meet the equally strainge house maid Magenta (Patricia Quinn), which leads into the infamous song "The Time Warp".
The Criminologist comes on and explains the steps to the 'Time Warp' dance.
Brad and Janet are ushered into a great hall with a throne and a jukebox at it's far end where conventionists of every size and description wearing tuxedos and party hats are dancing and singing the ('Time Warp'). During the song we are introduced to the gold-sequin-wearing, tap dancing Columbia (Little Nell). All of this is too much for Janet and Brad who try to sneak out carefully. Janet begs Brad to leave as the place is creepy, but Brad simply says that they should stay to watch more "folk dancing." Janet refuses as she's "cold, wet and just plain scared!", though Brad tries to reassure her.
Janet turns around to leave and sees Dr. Frank N. Furter (Tim Curry) in full drag regalia, wrapped up in a black cloak. She screams and faints. Frank introduces himself though a song as a ('Sweet Transvestite') from Transsexual, Transylvania". Brad asks him for help, explaining his plight, and Frank smirks and acknowledges that yeah, Brad needs help, and offers him a mechanic at first only to change his mind as "Maybe the rain isn't REALLY to blame" and instead decides to "remove the cause but NOT the symptoms."
Frank then goes into an elevator and rises upstairs to the applause of the partying conventionists. Riffraff and Magenta strip Brad and Janet down to their underwear. Brad and Janet then are prodded into the elevator and taken upstairs to Frank's laboratory.
Brad and Janet are led out into the center of an observing room where they are put on display by Dr. Frank N. Furter, now wearing a lab coat and long surgical gloves. The Transylvanian conventionists watch the events from an above balcony. Frank N. Furter then walks over to a box-like shape covered by a tarp and throws off the covering to reveal a tank. He shouts for Magenta and Riffraff to set the controls and start the machinery as the room darkens. Frank himself laughs maniacally as he turns knobs, dials, and wheels as fluids pour into the tank and a humanoid form appears slowly, skeleton first, much to Janet and Brad's terror.
Carefully, Frank N. Furter leads out the humanoid figure wrapped entirely in bandages and cuts them away to reveal a full-grown man with blond hair, tanned skin, blue eyes and a muscular figure wearing only a skimpy golden bikini over his crotch. Riffraff spins some wheels he shouldn't have while cackling to himself, setting the blond man, known as Rocky Horror (Peter Hinwood), loose. Frank chases Rocky through the lab crying his name as a bouncy song about the creation ('I Can Make You a Man'), Rocky feeling a sense of dread plays. Eventually Frank catches Rocky and scolds him for misbehaving, but says he forgives him as he's beautiful ('Sword of Damocles').
Then, the deep freeze malfunctions and Columbia squeals, "Eddie!" A burly, heavyset biker named Eddie (Meatloaf) rides out on a motorcycle, dressed in black leather, singing about his former glory ('Whatever Happened to Saturday Night?/Hot Patootie') The conventionists eat it up, enjoying the show, but Frank becomes wrathful that Eddie stole his thunder and takes out a pickax, chasing Eddie into the deep freeze where he is hacked to bits. This puts everyone, even the giddy conventionists into a shocked and somber mood. Frank, tires to pick things up by talking about how beautiful Rocky is in a song ('I Can Make You a Man, reprise'), leading away his new creation to a "bedchamber" in a wedding-style procession.
The Criminologist comes on again and mentions that Brad and Janet are in trouble now as they are being led away to separate rooms for the night.
While separated, Frank N. Furter comes into Janet's bedroom, dressed as Brad, and seduces Janet. Then he goes into Brad's room, dressed as Janet and tries to seduce Brad. Brad puts up a little bit of a fight, but is talked into it. Afterwards, Janet feels frightened and used and goes to look for Brad. Meanwhile, Rocky escapes from the bedchamber and is running loose, chased by dogs through the rain outside the castle by the gleeful Riffraff. While wandering the castle lost and afraid, Janet encounters Rocky hiding in his tank at the lab. Seeing that he's injured, she tears her petticoat to bandage his wounds, pausing as she realizes she's aroused.
The Criminologist comes on and mentions the complexity of human emotions and the dangers of lust. He fades away to Magenta and Columbia who are secretly watching Rocky and Janet in the tank via a monitor in their room.
Janet tries to seduce Rocky, explaining that she used to be a virgin, but now she finds she really likes sex and wants it NOW ('Toucha Toucha Touch Me'). Rocky is more than happy to oblige. Meanwhile, Columbia and Magenta watch in secret from the closed circuited TV, laughing and playing with one another, making fun of the events unfolding before them.
As the two women enjoy one another, Frank N. Furter beats up Riffraff for letting Rocky loose, while Brad watches with horror. An alarm goes off and Riffraff looks on another TV monitor and mentions that someone is outside by the main gate as they all look and see a middle aged man in a wheelchair buzzing the intercom at the front gate. Dr. Everett Scott (Jonathan Adams) has arrived at the castle. Brad recognizes his old teacher and is happy to see him, but Frank N. Furter is angry that the two know one another, recognizing Dr. Scott as a federal agent investigating UFOs, suspecting Brad and Janet are actually spies. Brad denies this, explaining that Dr. Scott is his science teacher from Denton High, but Frank doesn't believe him.
Meanwhile, Dr. Scott enters the castle and finds himself alone in the 'zen room' filled with various smoldering insence. Frank N. Furter takes Brad to the lab where he turns on a powerful magnet to drag Dr Scott's wheelchair up to them... with Dr. Scott still inside it. The clunk of Dr. Scott's wheelchair arriving wakes the sleeping Janet and Rocky who sit up in shock. Everyone in the room is frightened, confused and hurt to see one another here. Magenta appears up and announces that dinner is ready. Attempting to handle things with grace, Dr. Frank N. Furter dismisses everyone for dinner, informing them that formal attire is optional as he stomps off enraged.
Everyone meets in a grand dining room for a dinner of roasted beef and vegetables in honor of Rocky's Birthday. Frank demands that everyone sing Rocky "Happy Birthday." Dr. Scott reveals in a song ('Eddie's Teddy') that he's not here to investigate Frank and his household, but to look for his nephew, Eddie, who went missing with a cryptic cry for help in a letter being the last contact he had from him. Sure, Eddie was a no good kid, but he's still family. In response to this, the tablecloth is pulled off the table to reveal Eddie's hacked-up body in a glass case... and the fact that they were being served roast Eddie for dinner. Brad and Dr. Scott are paralyzed with terror, and Janet runs to Rocky's arms. Frank is outraged, slapping Janet. Janet runs away with Frank chasing after her, encouraging her through a song ('Once in a While') to stop sleeping with everyone else as she's now his.
Janet, followed by Frank N. Furter, Rocky, Brad, and Dr. Scott end up in the lab again. Frank pulls a switch to "glue" everyone's feet to the floor but his. Everyone tells Frank he's a "Hot dog." In response, he simply flips a switch and turns them all to stone. Columbia comes in and tells Frank he's gone too far this time as now people are really hurt. Frank N Furter simply responds by turning Columbia to stone, too. He then tells Riffraff and Magenta to prepare for the floor show.
The Criminologist comes on and hints that in this place where nothing's as it seems, the Floor Show is going to be something very shocking.
The next scene we see the statue versions of everyone on stage, now all wearing fishnets, makeup, a thong and the same bustier. One by one they are unfrozen, and they each sing and dance a song ('Floor Show') about how they've changed since they came here. Rocky and Columbia sing about their past times ('Rose Tint My World'). Frank N. Furter, Brad and Janet sing their own version ('Fanfare/Don't Dream It'). Dr. Scott is accidentally unfrozen and realizes that this place is a trap and everyone should run while they still are sane enough to escape. Frank N. Furter comes out like a prized showgirl and sings a solo, starting an orgy in a swimming pool that is uncovered as he sings. After the orgy, Frank N. Furter sings a song praising his wild and untamed household ('Wild and Untamed Thing').
This song, however is interrupted by Riffraff and Magenta, now wearing strange uniforms and armed with laser ray guns. Riffraff informs Frank that it's all over as his mission was a failure due to Frank becoming too extreme. He declares that Frank is now his and Magenta's prisoner as he has been made commander, and that they're going back to their home planet of Transylvania in the Galaxy of Transexual immediately. Frank is happy for this, singing about how long he's been wanting to go back to the homeland he was exiled from ('I'm Going Home'). Riffraff stops him again and explains that only he and Magenta are going home; Frank N. Furter is to be killed as Riffraff replies: "say hello to oblivion". Riffraff points a ray gun at Frank, but Columbia screams in an attempt to save Frank. Riffraff quickly turns around and kills her. Riffraff then kills Frank as he tries to run away. Rocky, seeing his creator fall, grabs Frank and climbs the set in the background of the stage, crying in rage and pain. It takes several shots from the ray gun, but Rocky is killed and falls into the pool where he and his creator float dead.
Riffraff turns to Brad, Janet and Dr. Scott and tells them to leave now while they still can and they do so. Meanwhile, in a now empty house, Magenta and Riffraff celebrate going home as an incestuous relationship is implied. Brad and Janet, carrying Dr. Scott, escape just as the castle explodes and flies away under a rainbow and blue skies of dawn back to Riffraff and Magenta's home planet, leaving Dr. Scott, Janet, and Brad writing on the charred ground, still in drag from the floor show as it flies away into space. (In some versions the three of them sing one final song about loss of innocence called 'Superheros'.)
The Criminologist comes back one last time with the somber, iconic lines describing the flying away of the house:
"And crawling... on the planet's face... some insects... called the human race. Lost in time... and lost in space.... and meaning."