Robert Godhigh rushed for two touchdowns and caught a third for Georgia Tech. Jamal Golden returned a kickoff 100 yards for a score, and backup quarterback Vad Lee rushed for 112 yards and two touchdowns and threw for a third.
The teams combined for 1,085 yards, 118 points - and just five punts - in surpassing the previous ACC record of 110 points set in Virginia's 63-47 victory over Tulane in 1968.
Georgia Tech outgained the Tar Heels 588-497 and set a school record for points in an ACC game, eclipsing its 63 against Wake Forest in 1998.
Bryn Renner threw two touchdown passes for the Tar Heels (6-4, 3-3).
The Tar Heels pulled to 58-50 on Renner's 11-yard touchdown pass to Quinshad Davis and Tim Scott's 32-yard interception return on the first play of the fourth quarter. Orwin Smith followed that with a 22-yard touchdown run to put the Yellow Jackets up 65-50.
Chris Tanner kicked a 34-yard field goal to complete the scoring with 3:40 left.
Smith finished with 83 yards rushing and 39 yards receiving. Starting quarterback Tevin Washington tied former teammate Joshua Nesbitt's ACC record for quarterbacks with his 35th career rushing touchdown, a 25-yarder on his team's opening series.
Lee, a native of nearby Durham, N.C., took over on Georgia Tech's third offensive series, immediately led three straight scoring drives and played the rest of the way. He finished 6 of 10 for 169 yards passing.
David Sims added an 11-yard touchdown run for the Yellow Jackets, one of four Coastal Division teams - along with North Carolina, Miami and Duke - with three league losses.
Romar Morris had a 30-yard touchdown run for the Tar Heels, and Renner finished 24 of 35 for 350 yards with an interception.
The second half started with a bang: two touchdowns - one by each team - in a 34-second span.
Golden put the Yellow Jackets up 34-29 when he returned the opening kickoff of the second half for a touchdown. Bernard then took a short pass from Renner and broke two tackles while turning it into his longest career reception, a 78-yard score that briefly gave the Tar Heels a 36-34 lead.
Godhigh followed that with a 4-yard TD that put Georgia Tech ahead to stay. Tanner kicked a 35-yard field goal to make it 44-36.
Bernard, the ACC's leading rusher, became the first Tar Heel rusher since Natrone Means to crack 1,000 yards in consecutive seasons.