In 1958 New York City, a waiter pages George Kaplan at the Plaza Hotel's Oak Room restaurant at the request of thugs. As advertising executive Roger Thornhill summons the same waiter, he is mistaken for Kaplan, kidnapped by the thugs, and brought to the estate of Lester Townsend in Glen Cove. He is interrogated by Phillip Vandamm, a Cold War spy against the United States, posing as Townsend. Vandamm arranges Thornhill's death in a staged drunk-driving crash. Thornhill survives, but fails to convince his mother or the police of what happened. Revisiting the estate, Thornhill learns Townsend is a United Nations diplomat.

Thornhill and his mother go to Kaplan's empty hotel room at the Plaza, where the thugs have followed him and begin their pursuit. Thornhill heads to the U.N. General Assembly Building to meet Townsend, who he sees is not Vandamm. One of the pursuing thugs throws a knife, killing Townsend, who collapses in Thornhill's arms. Thornhill is photographed as he grabs the knife, giving the appearance that he is the murderer; he then flees, attempting to find the real Kaplan. The United States Intelligence Agency realizes that Thornhill has been mistaken for Kaplan, but their chief, "the Professor", decides against rescuing him for fear of compromising their operation: Kaplan is a non-existent agent they created to confuse and distract Vandamm.

Thornhill sneaks aboard the 20th Century Limited train to Chicago, where he meets Eve Kendall, who hides him from the police. The two establish a relationship—on Kendall's part because she is secretly working with Vandamm—and she tells Thornhill that she has arranged a meeting with Kaplan at an isolated rural bus stop. Thornhill waits there, but is attacked by a crop duster plane. After taking cover in a cornfield, he attempts to halt a tank truck; it brakes, the airplane crashes into it, and he escapes during the aftermath of the explosion. Thornhill reaches Kaplan's hotel in Chicago and learns that Kaplan had checked out before the time when Kendall claimed she talked to him. Thornhill goes to her room and confronts her, but she leaves. He tracks her to an art auction, where he finds Vandamm purchasing a Mexican Purépecha statue.
Vandamm leaves his thugs to deal with Thornhill. To escape, Thornhill disrupts the auction until police are called to remove him. He says he is the fugitive murderer, but the Professor intervenes and tells him that Kaplan was a fiction and their real agent is Eve Kendall. Vandamm lives near Mount Rushmore and they think he will be leaving the country by plane from there.

Thornhill agrees to help maintain Kendall's cover. At the Mount Rushmore visitor center, now willingly playing the role of Kaplan, he negotiates Vandamm's turnover of Kendall to be arrested. Kendall then shoots Thornhill, seemingly fatally, and flees. Actually the bullets were blanks, to fool Vandamm. Afterward, the Professor arranges for Thornhill and Kendall to meet. Thornhill learns Kendall must depart on the plane with Vandamm and his henchman Leonard. He tries to dissuade her from going, but is knocked unconscious at the Professor's behest, and locked in a hospital room.

Thornhill escapes and goes to Vandamm's house to rescue Kendall. There he overhears that the sculpture holds microfilm and that Leonard has discovered the blanks remaining in Kendall's gun. Vandamm indicates that he will kill Kendall by throwing her from the plane. Thornhill manages to warn her with a surreptitious note. Vandamm, Leonard, and Kendall head for the plane. Thornhill is momentarily held at gunpoint until he realizes the gun is the one with blanks. As Vandamm boards, Kendall takes the sculpture and runs to the pursuing Thornhill. They flee to the top of Mount Rushmore. As they climb down the mountain, they are pursued by Vandamm's thugs, including Leonard, who is fatally shot by a park ranger. Vandamm is taken into custody by the Professor.

Meanwhile, Kendall is hanging on to the mountain by her fingertips. Thornhill reaches down to pull her up, at which point the scene cuts to him pulling her—now the new Mrs. Thornhill—into an upper berth on a train, which suggestively enters a tunnel.