Auburn freshman Wes Byrum made a 39-yard field goal to start overtime and then Grothe took over. He ran three times, including a sneak on fourth-and-1. Then, on the next play he hit Hester behind the defense for the game-winner.
South Florida (2-0), which had pulled off upsets of highly ranked West Virginia and Louisville in the past two seasons, won for the first time in five tries against Southeastern Conference teams.
The Tigers (2-0) committed five turnovers, but the Bulls couldn't turn any of them into points. Grothe made sure they didn't have to turn to struggling kicker Delbert Alvarado in overtime. He had missed four attempts in the second half.
Auburn gained only 2 yards on its overtime possession, with a run by Ben Tate and back-to-back incompletions by Brandon Cox. The teams had swapped late field goals to force the extra play.
Byrum kicked a 46-yarder with 2:54 left for a 20-17 lead after Cox completed 4-of-5 passes for 50 yards on the drive. But the Bulls quickly smothered the Tigers' excitement.
Jerome Murphy raced 59 yards down the left sideline on the kick return to Auburn's 32. The Bulls moved to Auburn's 2 on a run and two completions by Grothe, but had to settle for Alvarado's 19-yard field goal with 55 seconds left.
The Tigers let the clock run down after failing to move the ball on its next two plays.
Grothe completed 18-of-27 passes for 184 yards and also rushed for 31 yards and a touchdown.
Cox struggled badly most of the game, going 16-for-35 for 165 yards and two interceptions.
Both teams made plenty of mistakes to take the game to overtime.
Mike Jenkins picked off a pass by Cox and returned it to the Auburn 3 with 7:28 left to play after the Bulls tied the game on a 38-yard field goal by Alvarado.
But the Tigers pushed them back a yard on three plays and Alvarado missed a 21-yarder, his fourth miss of the second half -- including three potential game-tying kicks in the final 7 minutes of the third quarter.
Alvarado's first two attempts went wide left and his third was blocked by Sen'Derrick Marks.
Auburn redshirt freshman tailback Mario Fannin, who provided a spark early in his first career action on offense, fumbled on consecutive carries late inside Auburn's 25 to set up two of the attempts.
The Bulls had stunned the Auburn fans by jumping ahead 14-3 on a 2-yard touchdown run by Mike Ford -- a former Alabama signee -- late in the first quarter.