Tennessee (1-0) was led by running back John Kelly, who ran 19 times for 128 yards and four touchdowns. Quarterback Quinten Dormady completed 20 of 37 passes for 221 yards and two touchdowns, both to Marquez Callaway, who had four receptions for 115 yards.
Georgia Tech (0-1) got a record performance from quarterback TaQuon Marshall, who was making his first start. He ran 44 times for 249 yards and scored five touchdowns, the latter two both school records. Marshall also completed 5 of 9 passes for 120 yards.
KirVonte Benson rushed 26 times for 124 yards and one touchdown for the Yellow Jackets.
Kelly scored on a 2-yard run in the second overtime to make it 42-35, but Marshall answered with a 13-yard touchdown run. The Yellow Jackets tried to win it with a two-point conversion, but Marshall was stopped at the line and his desperation pass fell incomplete to end the game.
In the first overtime, Marshall scored on a 1-yard run and Tennessee responded with a 1-yard run from Kelly.
The momentum shifted in favor of Tennessee when the Vols took advantage of a turnover and tied the game at 28-28 with 1:29 left in regulation. The Volunteers got the ball when Georgia Tech's J.J. Green was stripped by Rashaan Gaulden at the end of an 18-yard run. The fumble was recovered by Tennessee's Micah Abernathy at the 7. Tennessee drove 93 yards and scored on Kelly's 11-yard run.
Georgia Tech drove into position to win the game at the horn, but Tennessee's Paul Bain got a hand on the 36-yard field goal try by Shawn Davis to send the game to overtime.
The Yellow Jackets scored on their first drive of the second half, with Marshall powering in from the 1 over the right guard for a 21-7 lead.
Georgia Tech appeared to be driving for another score when an illegal block penalty forced them to attempt a 47-yard field goal. But Davis, who won the kicking job this week, shanked the kick and Tennessee took over at the 30.
The Vols raced downfield and scored with 42 seconds left in the third period. Dormady connected with Callaway for a 10-yard touchdown in the right corner of the end zone to cut the lead to 21-14.
The two teams traded scores early in the fourth quarter. Marshall ran it in from 6 yards with 13:08 left and Tennessee answered with a 50-yard pass from Dormady to Callaway with 11:49 remaining.
The Yellow Jackets held a 14-7 lead at halftime.
Georgia Tech scored on its third possession, driving 86 yards in 12 plays to take a 7-0 lead. The Yellow Jackets began to run between the tackles to pick up consistent yardage. The big play on the drive was a 44-yard pass from Marshall to Ricky Jeune. The touchdown came on a keeper by Marshall from the 1.
Tennessee evened the score with 8:11 left in the half on a 1-yard dive by Kelly. The 46-yard drive was set up when Daniel Bituli knocked the ball away from Marshall and Cortez McDowell recovered the fumble for the Vols.
Georgia Tech ground out another score before the half, going 70 yards in 16 plays and seven minutes. Benson scored on a 1-yard run with 1:11 left in the half to give the Yellow Jackets a seven-point lead.