Ware had 43 yards rushing on nine carries for the Bulldogs (2-0, 1-0 SEC), who won last year's SEC championship over LSU. Thomas Brown rushed for 56 yards and Kregg Lumpkin ran for 36, as Georgia's three rotating tailbacks combined for 135 yards.
Georgia starting quarterback Joe Tereshinski left the game in the first quarter with an ankle injury. Freshman Matthew Stafford took his place and completed 8-of-17 passes for 171 yards and three interceptions.
Blake Mitchell completed 16-of-22 passes for 156 yards for the Gamecocks (1-1, 0-1), who have only scored one touchdown through their first two games this season.
Brandon Coutu kicked three field goals for Georgia.