The Scarlet Knights (3-3, 1-2 Big Ten) tied a school record by rallying from a 25-point deficit in the final 20½ minutes.
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Federico won it after having two extra points blocked.
Chris Laviano led Rutgers by going 28 of 42 for 386 yards with three touchdowns and one interception.
But it was a botched snap on a rare Indiana punt that turned the game. Kemoko Turay scooped it up and scored on a 26-yard return to make it 52-39.
Rutgers then took advantage of both of Nate Sudfeld’s interceptions to tie the score at 52.