After Georgia Tech's B.J. Elder hit 1-of-2 free throws with 0.5 seconds remaining to give the Yellow Jackets a 69-67 lead, Ron Slay fired a halfcourt pass to Higgins who launched the game-winner.
"Sometines those are best the kind of shots," said Higgins. "Slay threw a perfect pass and I just caught it and shot it."
The Vols battled back from a 62-49 deficit with 7:25 remaining to tie the game, 64-64, on a C.J. Watson three-pointer with 1:51 remaining.
Slay, the SEC's leading scorer, led Tennessee (3-1) with 28 points and 12 rebounds. Slay connected on 11-of-18 from the field, including 3-of-3 from three-point range.
B.J. Elder scored 21 points to lead Georgia Tech (4-2).
After falling behind by 13 to open the second half 12-2 Tech run, Slay led the Vols back to close the gap to four (49-45) at the 13:01 mark.
Despite outshooting and outrebounding the Yellow Jackets in the first half, Georgia Tech took a 35-32 advantage into the break. The Vols committed 14 first-half turnovers.
The rejuvenated Tennessee team will return to action Tuesday, hosting Charleston Southern in Knoxville at 7:30 p.m. (EST).