The film opens with a droll series of silent bits as a constable at night on his bicycle discovers a man with his hands on a rope with a strangled woman -- Margaret McGinty -- attached. As it happens Miss Marple (Margaret Rutherford) is on the jury in the succeeding murder trial. She forces a mistrial as the only one to hold out in a seemingly open and shut case because she views the evidence as circumstantial. She then enlists the aid of her friend Mr. Stringer (Stringer Davis, Rutherford's actual husband) to follow the evidence in support of her theory to find the real murderer. She is harassed by Detective Inspector Craddock (Charles "Bud" Tingwell) who wants her to get out of the way of the Police. She traces the evidence to a low-rent theatre troupe run by H. Driffold Cosgood (Ron Moody), and manages to infiltrate the acting company with a whirling rendition of The Shooting of Dan McGrew, and intimating that she may be willing to financially subsidize the company.
No sooner does she secure a place as an actress, than one of the actors, George, drops dead from poisoning and Detective Inspector Craddock shows up again to try to get her to give up her hunt, but does also work with her to discover the killer. She suggests that Craddock investigate bank accounts of all the actors to see who, if any, recently withdrew 100 pounds -- the amount of cash found surrounding the body of Mrs. McGinty and now believed to be a pay off for black mail. Back at the boarding house where all the actors are staying, Miss Marple continues to ferret out clues and finds a note outside her door telling her to meet someone at 1AM in the kitchen if she wants to find out more. As she is sneaking down the stairs, she sees middle-aged actress Dorothy sneaking down just ahead of her and follows. When she opens the closed kitchen door, Dorothy is dead on the floor and Mrs. Marple, smelling bitter almonds indicating cyanide, throws open the outside door and windows. When the inspector arrives, she explains that the murder was done in a complicated way involving an on/off stove timer, a pot containing candle wax and a cyanide capsule but says this was the murder method of the play that they are opening with the following week ("Out of the Stewpot"), so all the actors would know how to do this. Meanwhile, Mr. Stringer arrives and tells her that the police have learned that one of the actors DID withdraw 100 pounds recently, but it was the recently-murdered George. Inspector Craddock theorizes that George had been blackmailing Margaret McGinty, which is why he withdrew the 100 pounds from his account, and then, in a fit of remorse, killed himself, but Mrs. Marple thinks otherwise.
Mrs. Marple visits a theatrical agent who tells her that Margaret McGinty was in a 1951 play, "Forever September", written by Mr. Cosgood, along with a Rose Kane, who had a child about eleven. The agent says that Rose Kane was hanged for poisoning her husband, and Margaret McGinty, took the child in for awhile but that eventually it was sent on to an orphanage. He can't remember the sex of the child, but does recall the name, "Evelyn" pronounced "EEvelyn". This child would now be about the age of the four younger members of the acting troupe, Eva, Bill, Sheila, and Arthur.
As the play opens the next week, the police are on hand to protect Mrs. Marple, but Eva comes into her dressing room with a knife and together they go below stage where Mrs. Marple learns that Eva thinks that Mrs. Marple was involved in killing George, who, it turns out, was her lover. Just as Mrs. Marple talks Eva out of her ill-conceived murder plan, the real murderer comes out of the shadows causing Eva to drop her knife and run away in fear. The shadowy figure is revealed to be Bill Hanson. Bill explains that in the play he is in a closet and he has used the stage trap door to come down and will be able to murder Mrs. Marple, and return to his closet before his scene takes place in 3 minutes. Bill, is actually Evelyn Kane, and he murdered Margaret McGinty because she was going to reveal to his soon-to-be father-in-law Bill's mother's sordid past. He picks up Eva's knife (he had intended to strangle Mrs. Marple) but Mrs. Marple draws the revolver that is to be used in the play (she had replaced it with a banana), and points it at Bill explaining she has replaced the blanks with real ammunition. She announces she was a former pistol champion at Bisley but he still advances on her so she shoots in two a prop rope causing a heavy wooden wheel to fall and knock out Bill, but also Inspector Craddock who had rushed downstairs. At the same time, Mr. Cosgood steps into the open stage door and comes crashing down. As she looks around at the three unconscious men, she says "Oh dear, oh dear, oh dear". The movie ends with her visiting Cosgood and Inspector Craddock in hospital, where he announced he has been promoted to Chief Inspector. Cosgood tries to get her to fund his play, but she says that she is "no angel". Mr. Stringer picks her up in a horse-drawn cart and they ride away.