Before he became a star, Baker sang as a member of the Vitaphone chorus at Warner Bros.[2] At the height of his radio fame, and after leaving the Benny show in 1939 (succeeded by Dennis Day, whose tenor voice was very similar to Baker's), he appeared in 17 film musicals, including Mr. Dodd Takes the Air (1937), At the Circus (1939), and The Harvey Girls (1946).

He later co-starred with Mary Martin in the original Broadway production of Kurt Weill and Ogden Nash's One Touch of Venus (1943).

Baker first appeared on Jack Benny's weekly radio program on November 3, 1935,[3] having been hired to replace singer Frank Parker.

[5] Baker portrayed a high-voiced, innocent young man on the show, who would frequently cause the Jack Benny character frustration with his "silly" remarks.

Baker's final regular appearance on Benny's radio show aired on June 25, 1939,[6] leaving the $3,000 per week job because he no longer wanted to play the character.