Austin ran 98 yards for a touchdown and hauled in scoring strikes of 57 and 81 yards, becoming just the third player in NFL history with three touchdowns of 55 yards or more in a game.
Kellen Clemens tossed for 247 yards on 9-of-16 efficiency and Zac Stacy ran for 62 yards with a score on 26 carries for the Rams (4-6), who broke a three-game losing streak.
The AFC South-leading Colts (6-3) were victimized by three interceptions thrown by Andrew Luck, who finished 29-of-47 through the air for 353 yards and a touchdown.
The loss was worst at home for Indianapolis since 1993.
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