While aboard a Mexican cruise he takes frequently, auto executive Hayden Danziger (Robert Vaughn) has been having an affair with the ship's lounge singer Rosanna Wells (Poupée Bocar). When Wells threatens to expose their affair to Danziger's wife, Sylvia (Jane Greer), Danziger decides to get rid of her. To set up his alibi, he inhales some amyl nitrite to feign a heart attack in the swimming pool, so that he will be checked into the ship's infirmary. During a lapse in security, Danziger dons a crewman's uniform, sneaks out of his infirmary bed, and waits in Wells's cabin for her performance break. When she comes back, Danziger shoots her, plants evidence to implicate a band musician (Dean Stockwell), ditches the pistol and returns to the infirmary before the doctors can find him missing. Columbo, who happens to be enjoying the same cruise with his wife, is pressed into service by the ship's captain (Patrick Macnee). Bernard Fox and Robert Douglas also guest star.