Despite blowing a 15-point lead they held midway through the second half, the Yellow Jackets (10-6, 1-2 ACC) went ahead for good when Golden's 3-pointer from the left wing made it 70-68 in the final minute.
Golden gave Georgia Tech its biggest lead at 15, but the Irish went on a 16-3 run to tie the game at 57 on Atkins' three-point play.
Sherman missed his first nine field goal attempts, but hit six of his last nine shots, including a reverse layup to give the Irish a 68-67 lead with 1:15 remaining.
Georgia Tech began the game with a 10-26 ACC record under third-year coach Brian Gregory, but the Jackets led by as much as 13 in the first half on Marcus Georges-Hunt's 3 from the left key.
Notre Dame came within two in the first on Demetrius Jackson's layup at the 8:01 mark and on Steve Vasturia's with 1:17 remaining, but Golden hit a pair of free throws to make it a four-play lead at intermission.
The Irish, playing just their second away game of the season on an opponent's home court, trailed by as many as 15 in midway through the second half on Golden's runner from the baseline at the 13:59 mark.