Kurnitz grew up in Philadelphia and attended the University of Pennsylvania. Heentered journalism as a book and music reviewer for The Philadelphia Record in 1930. In his spare time he wrote fiction.

A mystery story Kurnitz wrote in 1937, Fast Company, about skulduggery in the rare-book business, led him to Hollywood. Metro-Goldwyn-Mayer bought the book,and Kurnitz wrote the screenplay. Kurnitz wrote more than forty movie scripts, among them Witness for the Prosecution, What Next, Corporal Hargrove?, and How to Steal a Million.

His first play was Reclining Figure, a 1954 comedy about painters and their patrons and the tricks of the dealers and collectors who prey on them. Later, Kurnitz wrote the hitcomedy Once More, with Feeling!. Other plays included High Fidelity and The Girl Who Came to Supper, a musical he wrote with Noël Coward, who composed the music and lyrics.

On March 18, 1968, Kurnitz died of a heart attack. At the time of his death he was working on a detective story.