Mann scored a career-high 29 points, including a three-point play with 2:25 remaining that gave Georgia the lead, and the Bulldogs beat Vermont 63-56 on Wednesday night in the first round of the NIT.
Georgia overcame a season-high 22 turnovers, including seven by Mann, which matched his high.
"Our ball-handling was terrible," Georgia coach Mark Fox said. "We talked about it at the half and did our best to correct it. It took us a while. The bus had to run over us before we decided to get back to who we really were all year, and I was concerned about that."
That "bus" was the visiting Catamounts, who trailed by 11 points early in the second half before taking a 47-38 lead with an 18-2 run.
Georgia (20-13) went 8 minutes without a field goal before Kenny Gaines' steal and fast-break layup ended the drought. The Bulldogs quickly regained the momentum.
Mann's basket and free throw gave Georgia a 56-54 lead. Marcus Thornton, who had 16 points, added another three-point play as Georgia ended the game with a 14-2 run.
Georgia will play Louisiana Tech, which beat Iona on Wednesday night, in the second round on Saturday.
"We hung in there and fought back, we just didn't have enough down the stretch," said Vermont coach John Becker, who said he was sad to see six seniors, including four starters, end their careers.
Mann (6-5, 210) caused matchup problems for Vermont's guards with his size and drives to the basket. Mann made 12 of 13 free throws.
"He has a lot of size for his position and he's a very good player," Carissimo said of Mann. "Credit him. He made his free throws and a lot of shots around the rim."
Free throws were the difference. The Bulldogs made 24-for-26 free throws, while the Catamounts made only six of 15.
"Unfortunately, we couldn't make free throws and we couldn't prevent them from getting to the free-throw line," Becker said.
Vermont fell to 0-3 in three NIT appearances.
Georgia took a 31-18 advantage in rebounds.
The turnovers began to mount from the opening minutes for Georgia.
"I think we came out somewhat flat early on," Thornton said. "We just got kind of lazy with the ball, made some careless mistakes, and did some things that are really uncharacteristic of us. Eventually we settled down, but that's something we've got to cut down if we want to keep winning games."