Thompson was summoned to start when regular Connor Shaw was idled with a sprained left foot and responded by passing for 315 yards, going 23-of-41 with one interception.
Ace Sanders racked up 118 yards with a score on six grabs and Bruce Ellington made two TD receptions for the Gamecocks (10-2), who defeated their intrastate rivals for the fourth consecutive time.
The victory was 65th at South Carolina for Coach Steve Spurrier, who moved past Rex Enright for the most in school history.
Tajh Boyd was intercepted twice for the Tigers (10-2), whose eight-game winning streak was snapped.
Swim Week Miami Beach 2014 [PHOTOS]