Damian Jones and Josh Henderson each finished with 12 points for Vanderbilt (7-3), which was coming off consecutive wins over Purdue and Western Kentucky.
Georgia Tech (8-2) has won five of six.
The Yellow Jackets made the right adjustments at halftime with the Commodores leading by eight, getting back on defense quicker and getting more production from their fast-break offense.
Georges-Hunt, Georgia Tech's leading scorer this season, was just 4 for 15 from the field, but in the final minute he hit a pair of free throws to make it 64-60 and grabbed a key defensive rebound when Wade Baldwin missed a 3 on Vanderbilt's ensuing possession.
With 6 seconds remaining, Luke Kornet tried to throw a court-length pass from Georgia Tech's baseline, but the ball was too high for Jones to handle at Vanderbilt's basket and bounced out of bounds.
Georgia Tech struggled against to get the ball inside against the Commodores' zone defense in the first half and struggled from the field at 27.8 percent.
But the Jackets began the second half on a 16-6 run to take their first lead since midway through the first half on Georges-Hunt's short jumper with 12:44 remaining.
Georgia Tech went up 47-43 on Mitchell's fast-break dunk about four minutes later. Mitchell's previous career high was 19 points against Delaware State last Dec. 29.
If the teams didn't like each other, it was evident in the second half when James Siakam and Jones blocked the ball hard out of bounds and celebrated on consecutive Georgia Tech possessions with Jackets leading 51-49.
A few minutes later, Georgia Tech guard Chris Bolden knocked Siakam down hard at the Vanderbilt baseline on a Commodores fast break and quickly turned his back to walk to the team huddle.
The foul wasn't hard enough to be called flagrant and Siakam hit two ensuing free throws to make it 53-all with 3:44 remaining.
After Mitchell's three-point play put the Jackets by four, Robert Sampson stole the ball from Shelton Mitchell and followed with a fast-break putback that gave Georgia Tech a six-point lead, its biggest of the game, with 1:16 remaining.
But the Commodores scored the next four points on the same possession as Wade Baldwin hit a free throw and Siakam grabbed the rebound when Baldwin missed his second attempt and converted a three-point play to make it 62-60.
Tech rallies past Vanderbilt, 65-60
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