The loss dimmed tournament hopes for the Bulldogs (14-11, 6-8), who are in fifth place in the East, one game behind fourth-place Vanderbilt.
Rolando Howell scored 10 points for South Carolina, but left the game and was taken to the hospital for X-rays after falling on his wrist early in the second half.
South Carolina scored eight straight points by four different players to go up 46-38 with 11:33 left on a layup by seldom-used reserve John Chappell, who was filling in for Howell.
Chappell, who scored four points on 2-of-3 shooting, got a standing ovation and the crowd chanted his name.
The Bulldogs pulled within three on Wright's 3-pointer with 10:26 left, but that was as close as they could get.
South Carolina went on a 14-1 run that was capped by the last of six foul shots by Gonner.
Georgia never trailed in the first half and led 31-30 heading into the locker room despite being outshot and having three players saddled with three fouls.