During his Service in the United States Army in World War II, Nelson debuted on the Broadway stage in one of the leading roles, Bobby Grills, in Moss Hart's play Winged Victory (1943). His next Broadway appearance was as Peter Sloan in Hart's Light Up the Sky (1948), which was a first-rate success. He went on to appear on Broadway with Barbara Bel Geddes in the original Broadway production of The Moon is Blue; he was the last surviving original cast member of the production. During the play's run he also starred in a CBS half-hour drama called The Hunter, premiering in July 1952. He played Bart Adams, a wealthy young American whose Business activities involved him in a series of adventures. He also appeared opposite Lauren Bacall in the Abe Burrows comedy Cactus Flower in 1965 and with Dorothy Loudon in The Fig Leaves Are Falling in 1969. Another Broadway role, that of Gus Hammer in The Rat Race (1949), kept Nelson away from the movies again, but after it closed he starred in the dual roles as Chick Graham and Bert Rand in The Man with My Face (1951), which was produced by Ed Gardner of radio fame.