Brice Johnson added 15 points and 11 rebounds for the Tar Heels (13-2, 2-0 Atlantic Coast Conference), who had fits with the Yellow Jackets (10-4, 0-1) all game. Georgia Tech led by nine points in the first half, by three at halftime and by one with 6 minutes left before the Tar Heels finally pushed ahead for good.
Berry's 3 was part of a 9-0 burst, and he followed with a driving basket for a three-point play on the next possession.
Marcus Paige added a key pull-up basket during the Tar Heels' finishing kick of scoring on 11 straight possessions, which ended when they ran out the clock on the final play.
Marcus Georges-Hunt matched his career high with 25 points for Georgia Tech.
Adam Smith added 20 points with six 3-pointers for the Yellow Jackets, who haven't beaten North Carolina since January 2011 and haven't won in Chapel Hill since a year before that.
The Tar Heels ended up with six players in double figures Saturday, helping them shoot 58 percent after halftime and 51 percent for the game.
The Yellow Jackets managed to keep the Tar Heels from getting out in transition early by converting an unusually high number of turnovers from UNC into points while getting several tough shots from Smith to build their own momentum.
Georgia Tech grabbed its biggest lead at 35-26 on Quinton Stephens' jumper with 4:22 left in the half and took a 42-39 halftime lead behind 14 points from Smith.
The Tar Heels eventually chased down the Yellow Jackets with a strong charge out of the break. Isaiah Hicks knocked down a turnaround jumper to tie it, then Nate Britt penetrated to find Johnson for a dunk and a 59-57 lead at the 11:54 mark -- UNC's first lead since 15-13.
UNC: Paige finished with 13 points. ... Senior center Joel James matched his career high with 11 points on 5-for-6 shooting. ... Junior forward Kennedy Meeks missed his sixth straight game with a bone bruise on his left knee. It's unclear when he'll be ready to return.
UNC plays at Florida State on Monday.