The game began at 11:30 a.m. to accommodate approximately 4,000 students from nearby elementary schools.
Georgia (3-7) took a 10-point lead, its biggest of the game, on Mann's putback dunk with 3:24 remaining.
Caldwell-Pope finished one rebound shy of his third straight double-double.
Langston Hall's runner with 4:32 remaining cut Georgia's lead to four, but Mercer never got any closer.
Neither team shot the ball well.
The Bears, who entered the game ranked No. 270 in Division I field-goal percentage, shot just 31.4 percent. Their 49 points were 9.3 under their average. Mercer was just 1 of 11 on 3-point attempts in the first half.
Georgia, which ranked 297th in field-goal percentage at tipoff, shot only 43.2 percent. But the Bulldogs outrebounded the Bears by 10.
Mercer began the season as the favorite to win the Atlantic Sun Conference after winning 27 games last year. The Bears, who won at Florida State on Dec. 2, visit Alabama on Saturday.
Georgia hosts Southern Cal on Saturday.
Florida State's student government has passed a resolution discouraging Seminoles fans from wearing Native American headdresses at games.
The second annual Gavitt Tipoff Games, eight games between members of the Big East and Big Ten to be played Nov. 14-18, will feature Villanova at Purdue in the opener.
Michael Lewis is leaving his assistant coaching job at Butler to take the same position at Nebraska under Tim Miles.