Mays was born on March 10, 1913, and developed his skills through regional sprint car racing, winning championships in the mid-1930s. He made his Indianapolis 500 debut in 1934 and immediately demonstrated top-level pace, claiming the pole position the following year in 1935.
Mays won the Indianapolis 500 pole in 1935, 1936, 1940, and 1948 — four poles in total, a mark of consistent one-lap speed across more than a decade of competition. He finished second in the 1940 and 1941 editions of the race. His strongest championship seasons came in 1940 and 1941, when he claimed back-to-back AAA National Championships, establishing himself as the best driver in American open-wheel racing at the time.
The Second World War suspended racing from 1942 through 1945, a pause that almost certainly deprived Mays of what would have been the peak years of his career. He returned to competition in 1946 and remained competitive, winning the Indianapolis pole again in 1948, though mechanical problems ended his race that year.
On June 6, 1948, during a race at Milwaukee State Fairground Park, driver Duke Dinsmore brushed the wall and was thrown onto the dirt track surface. With Dinsmore lying in the racing line, Mays made the deliberate decision to steer his car into the brick wall rather than risk striking the fallen driver. The impact destroyed Mays' car but Mays was uninjured, and Dinsmore was taken to hospital where he was found to have a fractured forearm and was reported out of danger. A memorial plaque was later placed at the Milwaukee circuit's south turn to commemorate the act. The race run there from 1950 to 1987 carried the name the Rex Mays Century in his honor.
On November 6, 1949, Mays started second on the grid at Del Mar Fairgrounds alongside Jimmy Davies. On the thirteenth lap, while under challenge from Johnnie Parsons, his car spun in the southeast turn and struck and destroyed 300 feet of spectator fencing before being launched back onto the track. Mays was ejected and, lying on the racing surface, was struck by three following cars driven by Paul Russo, Hal Cole, and George Connor. He was declared dead by the time an ambulance reached him. The Deputy Coroner confirmed he was killed on impact.
His funeral was held on November 10 at the Church of the Recessional in Forest Lawn Memorial Park, attended by hundreds of mourners including Pop Myers, vice president of the Indianapolis Motor Speedway, and numerous fellow drivers. Johnnie Parsons, who had been involved in the accident, also attended. The 22nd Agricultural Association, operator of Del Mar Fairgrounds, permanently banned all auto racing at the facility following the tragedy.
Mays' estate was valued at just under $12,000 at the time of his death. His will directed that racing equipment be sold and the proceeds placed in trust for his two children. Beyond his two national titles and four Indianapolis poles, his legacy was shaped by the Milwaukee incident, remembered as a defining act of driver character. Riverside International Raceway held the Rex Mays 300 in his name from 1967 to 1969, with Dan Gurney winning the first two editions and Mario Andretti the third.
Mays was inducted into the Auto Racing Hall of Fame in 1963, the National Sprint Car Hall of Fame in 1990, the International Motorsports Hall of Fame in 1993, and the Motorsports Hall of Fame of America in 1995.