It just hasn't figured out how to do so convincingly.
For awhile on Saturday, it appeared the Bulldogs were on their way to their first blowout win of the season. But a late-game lapse resulted in a 68-59 over Arkansas State that wasn't that close for most of the game.
For a program that's had one winning record in the past six seasons, it's become a pleasant problem.
"I've talked to the team about this: As you become a better basketball team, you're going to be ahead more often than you're behind. And you're going to have to learn how to play with a lead," head coach Mark Fox said. "As this team, as this program develops, hopefully we'll be in that position more often. Last year we weren't."
Saturday was the first of a five-game stretch against weaker opponents that leads up to the start of SEC play. So far this season, Georgia (7-2) has won three times by two points, and twice by three points.
The win over Arkansas State matched the Colorado game for Georgia's largest margin of victory.
But the Bulldogs led by as many as 21 early in the second half. At that point their energy level, so high in the midpoint of the game, returned to the level it had been at the start.
Arkansas State cut the lead to seven with 1:30 left. Then Jeremy Price made an offensive rebound with a minute left, but threw it away. He atoned for it on the other end, stripping the ball away to finally put the game away.
"We've still gotta grow as a team and learn how to play with a lead," Thompkins said. "Playing with so many guys that can put the ball in the basket we've become complacent and feel like our offense is gonna win games for us. And we stop guarding."
Thompkins led the Bulldogs with 15 points and seven rebounds. Travis Leslie (14 points and eight rebounds) and Dustin Ware (nine points and seven assists) had big games too, as did senior Chris Barnes, with a season-high 12 points.
Georgia sat on a 25-24 lead for awhile, as Arkansas State failed several times to grab the lead.
Finally, Gerald Robinson made a driving layup, and the play seemed to inject some energy into the team. The Bulldogs led by nine at the half.
The Bulldogs then started the second half on a 10-1 run, and eventually led 55-34.
"They're going to win some games, especially when league play starts," said Arkansas State coach John Brady, the former LSU coach. "They're a tough team, and will create some matchup problems for a lot of teams."
"We didn't play the full 40 minutes well," Fox said. "But we did play well enough in stretches to leave here today with a seventh win. So that part makes me feel good."