The 62nd International 500 Mile Sweepstakes was held at the Indianapolis Motor Speedway in Speedway, Indiana on Sunday, May 28, 1978. Danny Ongais dominated the early stages of the race but eventually dropped out with a blown engine. Al Unser, Sr. dominated the second half, and held a large lead late in the race. However, Unser bent his Lola's front wing during a pit stop on lap 180, causing his handling to go away over the final 20 laps. Second place Tom Sneva charged to catch the crippled Lola but came up 8 seconds short at the finish – the second-closest finish in Indy history to that point. Unser held off the challenge, and became a three-time winner of the 500.

Al Unser, Sr. entered the month having won the 1977 California 500 at Ontario the previous September. Later in the 1978 season, Unser would go on to win the Pocono 500 and the California 500, sweeping the "triple crown" of Indy car racing. As of 2016 he is the only driver in history to do so in the same season, and coupled with the win at Ontario in 1977, set a record by winning four straight 500-mile Indy car races.

Second year driver Janet Guthrie finished ninth, and it was later revealed she drove with a broken wrist. It was the highest finish for a female driver in Indy history until Danica Patrick in 2005. During time trials, Tom Sneva, who had broken the 200 mph barrier a year earlier, bettered his own record. This time he managed to complete all four qualifying laps over 200 mph, setting once again new one and four lap records.

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