Dorham began playing trumpet in high school, attended Wiley College (Marshall, Texas), and was on a U.S. Army boxing team in 1942. In 1945–48 he played in a series of big bands, including those of Dizzy Gillespie (Gillespie, Dizzy), Billy Eckstine (Eckstine, Billy), and Lionel Hampton (Hampton, Lionel), before joining Charlie Parker (Parker, Charlie)'s quintet (1948–49). A cofounder of the cooperative Jazz Messengers quintet (1955–56), he played in the Max Roach (Roach, Max) quintet (1956–58) and freelanced as a sideman, leader, and film score composer. Later he led groups together with Joe Henderson (1962–63) and Hank Mobley (Mobley, Hank) and studied at the New York University graduate school of music. Declining health eventually curtailed his playing career; by the late 1960s he was doubling as a jazz journalist for Down Beat magazine.

Dorham's fleet technique and fertility of invention made him popular in bebop circles. Though influenced by Gillespie, Fats Navarro (Navarro, Fats), and Miles Davis (Davis, Miles), he became a distinctive stylist who featured long, flowing melodic lines. His attack was precise and his trumpet sound was uniquely rich and clear; the warmth of his playing is especially well documented in the recordings he made for the Blue Note label as leader and sideman.