Rose competed at Indianapolis beginning in 1933 and was a regular presence at the Speedway throughout the following decade. Despite consistent participation, his first Indianapolis 500 pole position did not come until 1941, when he put his Maserati at the front of the grid. That race ended in disappointment when spark plug problems sidelined his car after just sixty laps.
However, the 1941 race would still belong to Rose. After his own car retired, he took over the Wetteroth/Offenhauser machine that Floyd Davis had started from 17th on the grid. Rose drove the co-driven car to victory, earning his first Indianapolis 500 win in unusual and dramatic fashion.
In 1947 and 1948, Rose won consecutive Indianapolis 500s behind the wheel of one of the Blue Crown Spark Plug Specials — Diedt/Offenhauser-powered cars owned and prepared by veteran driver and car owner Lou Moore.
The 1947 race produced one of the most debated incidents in Indianapolis history. Late in the running, Rose found himself second behind his rookie teammate Bill Holland when both were shown a sign reading "EZY" from the pits. Holland slowed in response, believing Moore was signaling that he held a comfortable lead of more than a lap. Rose, however, ignored the instruction and kept pushing. Rose closed in on Holland, and Holland — believing he had the race comfortably in hand — ceded the position without a fight, even offering a friendly wave as Rose passed to take the victory. Holland was furious afterward upon realizing he had been only seconds ahead, not a lap. The episode caused lasting tension between the two drivers.
The 1949 race brought a reversal. Rose again ran second to Holland late in the race and again set out to overtake his teammate despite Moore's "EZ" signals from the pits. This time Rose's car broke down under the strain while Holland drove home to win uncontested. Moore fired Rose on the spot after the race for disobeying team orders.
Rose made his fifteenth and final Indianapolis 500 start in 1951. He was knocked out of the race by an accident after 126 laps, and the 45-year-old driver subsequently retired from competition. In 1967, the Indianapolis Motor Speedway honored Rose by inviting him to drive the pace car for that year's race.
Rose worked for General Motors both during and after his active racing career. He was significantly involved in the development of the Chevrolet Corvette as a competitive racing machine. Off the track, Rose channeled considerable energy into humanitarian work: both of his children were affected by polio, and he considered his most important achievement to be the invention of a device enabling people without the use of their legs to drive an automobile.
The AAA/USAC-sanctioned Indianapolis 500 was included in the FIA World Drivers' Championship from 1950 through 1960, meaning drivers competing at Indianapolis during those years were credited with World Championship participation. Rose started two World Drivers' Championship races at Indianapolis, finishing in the top three once and accumulating four World Drivers' Championship points.
Rose was inducted into multiple motorsport halls of fame across his lifetime and posthumously, including the Auto Racing Hall of Fame (1967), the International Motorsports Hall of Fame (1994), the Motorsports Hall of Fame of America (1996), and the International Jewish Sports Hall of Fame (2007). He also received an Automotive Hall of Fame Distinguished Service Citation in 1966.