Curtis' theatrical career began in 1955 as a Broadway stage manager. His first appearance as a performer was in a 1965 revival of You Can't Take It with You. In 1971, he was awarded the Tony Award for Best Featured Actor in a Musical for The Rothschilds. Additional Broadway credits included The Cherry Orchard, A Patriot for Me, Via Galactica, Annie, Night Watch (played Curtis Appleby in 1972 production) and La Cage aux Folles.