Bulldogs freshman Anthony Edwards scored 36 points on 11-of-22 shooting, pulling down seven rebounds with four assists.
There were 17 lead changes and 21 ties in the game.
The Bulldogs had three players foul out, including two of their top rebounders in Rayshaun Hammonds (13 points, nine rebounds) and Toumani Camara (10 points, six rebounds).
Senior Jordan Harris fouled out despite playing just 10 minutes in a game that featured 56 fouls between the teams.
South Carolina had a 91-86 lead with 22 seconds left, but Georgia battled back and extended the game.
The Bulldogs had a chance to tie or win when Jermaine Couisnard spit a pair of free throws with 4.1 seconds left.
Wheeler took an inbounds pass near half court and drove the lane, finding contact. The whistle went in favor of the home team.
The Gamecocks made 9 of 13 free-throw attempts in overtime, while Georgia was just 3 of 6 in overtime.
The Bulldogs forced the overtime when Edwards hit two free throws with 7.5 seconds left to tie the game at 79.
Edwards scored 32 of his points in regulation, including 10-of-10 shooting from there free-throw line.
Georgia returns to action at 6 p.m. on Saturday at Stegeman Coliseum against Arkansas.