Johnny O'Bryant finished with 16 points and 14 rebounds as LSU (9-6, 0-4 Southeastern Conference) lost its fourth straight. The Tigers committed 21 turnovers and handed out just six assists. They shot just 36 percent (18 of 50) from the field.
Anthony Hickey scored 12 points and grabbed six rebounds for the Tigers.
Georgia (7-10, 1-3) desperately needed to win to avoid potentially dropping its first five SEC contests with games next week at home against No. 10 Florida and Saturday at Texas A&M.
Caldwell-Pope, who is fourth in SEC scoring average (16.8 points per game coming in), has led Georgia's scoring in all but two games this season.
LSU played without starting senior guard Charles Carmouche, who made the trip but couldn't play because of sore knees.
Georgia led by eight with 16:49 remaining on a three-point play by Williams, but the Bulldogs struggled with LSU's full-court press midway through the second half with three turnovers and three straight missed 3s by Caldwell-Pope.
Those mistakes helped the Tigers to reclaim the lead when Hickey hit consecutive 3s to make it 47-45 at the 11:10 mark.
Caldwell-Pope put Georgia back ahead 54-48 with a fast-break dunk and a layup that forced LSU coach Johnny Jones to call timeout with 7:24 remaining.
Shavon Coleman responded with a straightaway jumper that cut the lead to two, and Nemanja Djurisic's turnover on a 5-second call for failing to inbound the ball in time caused Bulldogs coach Mark Fox to call timeout.
Georgia went 4 minutes without a field goal before Brandon Morris fed Williams in the lane for a basket that caused Malik Morgan to foul out. Williams hit the ensuing free throw, and the Bulldogs led 57-54 with 3:25 to play.
Caldwell-Pope scored Georgia's next four points on a jumper and a pair of free throws, and Vincent Williams hit two free throws to give the Bulldogs a seven-point lead with 50 seconds remaining.
Nike Men's LSU Tigers Anthracite ELITE Stripe Performance Full-Zip HoodieShop
Maryland point guard Melo Trimble, considered a lock to leave the program before struggling in the second half last season, has withdrawn from the NBA draft and will return for his junior season.
Louisville's Chinanu Onuaku, who recently underwent a medical procedure to correct a heart rhythm issue detected during the combine, will keep his name in the NBA draft pool.
Andrew White III will return to the Nebraska men's basketball team next season after removing his name from the NBA draft.