He made his Indianapolis 500 debut in 1934 and won the pole in 1935, 1936, and again in 1940 and finished second, he returned the next year and finished second again. Mays won the AAA National Championship in 1940 and 1941. However, World War II suspended racing until 1946, denying Mays of what likely would have been the peak of his career. After the war, Mays again won the Indy pole in 1948 but was knocked out by a mechanical problem.
He was killed at the age of 36 in a crash during the only Champ Car race held at Del Mar Fairgrounds race track in Del Mar, California in November 1949. In this accident, Mays swerved to miss a car that had crashed in front of him. His car went out of control and flipped, throwing Mays to the track surface, where he was hit by a trailing car.
In his honor, the June race at the Milwaukee Mile was called the Rex Mays Classic from 1950 to 1987.