The Bulldogs (13-14, 7-7 Southeastern Conference) snapped a three-game losing streak.
Bruce Ellington finished with 11 points and was the only player to score in double digits for South Carolina (13-14, 3-11).
After Ellington's 3-pointer with 1:43 left in regulation made it 51-47 and gave South Carolina its biggest lead, the Gamecocks failed to score another field goal for the remainder of the game.
Georgia overcame an atrocious performance on free throws, missing 18 of 46 attempts, but South Carolina hardly helped itself by shooting 50 percent on 24 attempts.
The Bulldogs went over 6 minutes without a field goal before Caldwell-Pope's 3 with 11 seconds remaining made it 53-all. Ellington missed a long 3-point attempt at the regulation buzzer, but South Carolina got a second chance after the officials ruled that the game had gone to overtime.
During the timeout before the start of extra period, officials retracted their decision after replays that showed the clock had started too early after Caldwell-Pope's 3.
With another 4.5 seconds left in regulation, Ellington had his 3-point attempt from the right wing tipped by Mann at the buzzer.
In overtime, Caldwell-Pope hit a runner to give the Bulldogs a 55-53 lead, and Georgia never again trailed.
Caldwell-Pope, the SEC's second-leading scorer, finished just 4 for 12 from the field, including 2 for 8 on 3-point attempts. He was scoreless in the first half.
Ellington's 3 made it 37-35 with 12:17 remaining before Brian Richardson's 3 gave the Gamecocks their first lead at 39-38 with 8:47 left in the game.
South Carolina went up 51-47 on Lakeem Jackson's short jumper and Ellington's straightaway trey.
Eric Smith's two free throws gave the Gamecocks a 53-50 advantage with 17 seconds left in regulation before Caldwell-Pope sent the game to overtime with a 3-pointer from the right wing.
The Gamecocks were seeking consecutive wins for the first time since they beat Presbyterian Dec. 29 for their fifth straight victory.
South Carolina missed 18 of its first 21 shots in the first half.
Caldwell-Pope was 0 for 4 from the field and 0 for 3 on free throws before his two fouls shots put the Bulldogs up 28-18 early in the second half.
Georgia didn't fare much better in the first half, shooting just 23.1 percent to lead 23-16 at intermission.