The 25th International 500-Mile Sweepstakes was held at the Indianapolis Motor Speedway on Monday, May 31, 1937. With temperatures topping out at 92°F, it is one of the hottest days on record for the Indy 500.

Late in the race, Wilbur Shaw held a comfortable lead, and had lapped second place Ralph Hepburn. With about 20 laps to go, however, Shaw's car had been leaking oil, and had nearly lost nearly all of the oil out of the crankcase. In addition, the right rear tire was heavily worn. Shaw slowed down considerably in an effort to nurse his car to the finish line. Shaw and his riding mechanic John "Jigger" Johnson were both suffering from burns due to the leaking oil. Second place Hepburn realized Shaw's problems, and began a charge to catch him. He unlapped himself, and went on a tear in hopes of victory.

As the laps dwindled down, Ralph Hepburn was closing dramatically. Shaw was largely defenseless, as he was carefully nursing the car around. As the car went in and out of the turns, the oil pressure was rising and dropping, and Shaw was calculating how much time he could give up per lap and still maintain the lead. Hepburn closed to a straightaway deficit, then was nearly in reach. On the final lap Hepburn pulled to within a few seconds, and by the last turn he was directly behind Shaw and looking to pass him for the win.

With nothing to lose, Shaw floored the accelerator and pulled away down the final straight. He held off Hepburn for the win by 2.16 seconds, the closest finish in Indy 500 history to that point. The margin would stand as the closest finish ever at Indy until 1982.

Ten-lap (25 mile) qualifying runs were utilized. During the time trials held on May 28, the car of Overton Phillips burst into flames when his crankshaft broke and punctured the gas tank. He then crashed into the pit area, killing spectator George Warford of Indianapolis. Injured were Phillips and his riding mechanic, Walter King, Anthony Caccia, the brother of Joe Caccia, who died in practice for the 1931 race, and Otto Rohde of Toledo, Ohio, a crew member for Champion Spark Plug. Rohde succumbed to his injuries on June 1, 1937.

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