Georgia (8-6, 2-0 Southeastern Conference) made only 15 of 46 shots from the field (33 percent). Alabama (7-8, 1-1) also struggled, making only 37 percent of its shots.
Gaines set a career scoring high. Mann, who made 13 of 17 free throws, finished two points below his career high for the Bulldogs, who beat No. 21 Missouri in their SEC opener on Wednesday. No other Georgia player scored in double figures.
Trevor Releford led Alabama with 17 points, including 15 in the second half. Rodney Cooper had 15 and Shannon Hale had 14.
Marcus Thornton scored the first basket of the second half to give Georgia its biggest lead at 41-28.
Releford, who had only two points in the first half, helped lead Alabama's comeback attempt. His layup with 7:37 remaining cut Georgia's lead to 46-43. The Crimson Tide would come no closer than that.
The Bulldogs, who scored their next nine points on free throws, quickly pushed the lead back to seven points.
The first half was a scoring showdown between Gaines and Hale. Gaines made four 3-pointers in the first 20 minutes and had 16 points at the break. Hale, a freshman averaging 5.3 points per game, scored 11 of Alabama's first 13 points and added a late basket for 13 points in the half.
There were four ties in the half, the last at 15-15. Georgia then pulled away with a 14-4 run to lead 29-19 before stretching the halftime advantage to 11 points at 34-23.
Thornton had nine points and eight rebounds.
Georgia's previous worst field-goal percentage for a game was 38.3 percent in a 58-49 win over Gardner-Webb.
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