The film opens in a Montreal apartment on a cold winter morning, where Lisa (Samantha Jones) waits for an old man to sew bags of heroin into the cloth body of a rag doll. As Lisa leaves the apartment with the doll, we see the man watching her leave, then dialing someone on the phone. Lisa takes the doll with her on a flight to New York City, but when, on disembarking, she sees a man watching her, she becomes worried and gives the doll for safekeeping to fellow passenger photographer Sam Hendrix (Efrem Zimbalist Jr. ).
The man who'd been watching Lisa then roughly escorts her away. Later, when Lisa calls Sam to ask for the doll, Sam and his wife are unable to find it. Some time afterward, small-time con artist Mike Talman (Richard Crenna) and his partner Carlino (Jack Weston) arrive at the basement apartment where Sam lives with his blind wife, Susy (Audrey Hepburn). The two men watch until both the apartment's occupants have left, then enter.
They have an appointment with Lisa, who'd been their partner in crime prior to the recent imprisonment of both, but they are met instead by Harry Roat, Jr. (Alan Arkin), whom the audience recognizes as the man who watched and met Lisa at the airport. He offers them $2,000 each if they find Lisa's doll, which is somewhere in the apartment. After discovering Lisa's dead body hanging in a garment bag, Talman and Carlino want to make a quick exit, but Roat points out that they have left their fingerprints all over the apartment, while he has worn gloves.
Roat is then able to prevail upon the two to help him dispose of Lisa's body (he claims that he killed her because he caught her going into business for herself). Roat orders Talman and Carlino to help him try to find the heroin-stuffed doll. The next day, Susy's neighbor leaves for the weekend, and Sam leaves on a business trip. Once Susy is alone, the criminals begin an elaborate con game: In order to gain entry into the apartment, Talman arrives posing as a friend of Sam's, Carlino poses as a police officer, and Roat poses first as an old man and then as the man's son. Using first an innocuous story about Sam and the doll, then a darker one implying that Lisa has been murdered and that Sam will be suspected, the men persuade Susy to help them find the doll.
Talman gives her the number of the phone booth across the street as his own after falsely warning her of a police car stationed outside. Susy meanwhile has grown suspicious of Carlino and Roat, and Gloria (Julie Herrod), a neighbor who is paid by Susy to help her with errands, has been going in and out of the apartment, sometimes without Susy's noticing. After Talman leaves, Gloria sneaks into the apartment carrying the doll, which she stole earlier. She tells Susy there is no police car outside, and Susy discovers the doll. Wanting to confirm her suspicions about Carlino and Roat, Susy tells Gloria to go home and watch the phone booth that is next to Roat's van parked outside. If a man goes into it, Gloria is to phone Susy, let the phone ring twice, and hang up.
Gloria tells Susy she can signal her by banging on the pipes. On Carlino's next visit, after he calls Roat at the phone booth, Gloria sends Susy the telephone signal, and she sends the signal a second time after Susy calls Talman to tell him she has the doll. Finally realizing that Talman is a criminal in cahoots with the two others, Susy hides the doll. When he walks in with Corlino and Roat following quietly, she tells him the doll is at Sam's studio.
The three criminals leave after Roat cuts the telephone cord. When Susy bangs on the pipes, Gloria comes in and Susy sends her to the bus station in a taxi to wait for Sam. When Susy discovers that the telephone cord has been cut, she prepares to defend herself by putting the criminals in the dark along with her, breaking all the light bulbs in the apartment's light fixtures. She also pours a chemical into a bowl. When Talman returns, she refuses to cooperate when he demands that she hand over the doll. Talman has spent the most time with Susy and he has come to admire her for her quiet strength and ability to stand up to the three criminals despite her disability. He admits to her that he and his confederates are part of a criminal plot and that Sam, as Susy suspected, is completely innocent of any involvement, while Roat is a particular danger.
Susy needn't worry, though, Talman says, as he has sent Carlino to kill Roat. However, having anticipated that the others would turn on him, Roat has instead killed Carlino by running him over. As Talman prepares to leave, pausing to say something to Susy as he stands in the doorway, Roat suddenly appears and stabs him in the back. Intent on acquiring the doll, Roat chains the door shut in the dark apartment, pours gasoline on the floor, and sets a piece of newspaper on fire. A desperate battle follows in which Susy throws the chemical solution in Roat's face and forces him to put out the fire as well as smashes the last lightbulb in the apartment. The battle ends when Roat obtains light by opening the refrigerator, whose door he props open with a rag in the hinge. Susy, weeping (because she forgot about the refrigerator light), pulls the doll out of its hiding place and hands it to Roat. While Roat cuts open the doll and gloats over the treasure inside, Susy is able, unnoticed by him, to arm herself with a butcher knife.
Roat then announces his intention to rape Susy, but, as he leads her to the bedroom, she manages to stab him in the belly. As she stumbles across the floor toward the kitchen window to scream for help, Roat leaps out from the darkened bedroom and grabs her ankle. Screaming, Susy wrenches free, but the dying Roat doggedly pursues her, using the knife with which she stabbed him to drag himself across the floor. Susy is at the refrigerator, trying to close its door and thus extinguish its light, unaware of the rag that is preventing its closure. She then gropes for the refrigerator's cord, murmuring desperately, "Where is it?" As the reeling Roat stands with his last strength and staggers toward her with the knife, the refrigerator light finally goes out, and Susy's scream merges with the sound of a police siren.
The scene switches to the arrival of police cars outside the apartment. When the police enter with Sam and Gloria, Sam finds an unbroken light bulb, and we see the room littered with the bodies of Talman and Roat, but no Susy. Finally, as Sam calls out for her, the door of the unplugged refrigerator moves, and Susy emerges from behind it, shaken but alive..