Mance was born in Evanston, Illinois, and studied in Chicago. His first professional engagements were with Gene Ammons and Lester Young, and after his draft in 1953, Mance would play with musicians as they came through Chicago, such as Charlie Parker and Coleman Hawkins. Mance moved to New York and worked with Dinah Washington and Cannonball Adderley, before leading his own group for recording sessions for Verve and other labels. In later years, Mance taught at the Manhattan School of Music, and his bluesy style found many disciples, including Brad Mehldau. Mance passed away in New York aged 92.