North Carolina scored the first two touchdowns and held leads of 13-0 and 20-7 in the first half.
Georgia Tech (3-0, 2-0 Atlantic Coast Conference) earned its eighth straight home win in the series. North Carolina (1-2, 0-1) has not won at Bobby Dodd Stadium since 1997. Overall, Georgia Tech has won eight of the last nine in the series.
Vad Lee's 1-yard run gave Georgia Tech its first lead at 21-20 in the third quarter. Sims' 6-yard scoring run added to the lead early in the fourth quarter.
Georgia Tech had 324 yards rushing, including 100 yards on nine carries for Robert Godhigh.
Bryn Renner threw touchdown passes of 19 yards to tight end Eric Ebron and 24 yards to Sean Tapley after a 4-yard scoring run by Romar Morris.
The Tar Heels didn't score again after Tapley's touchdown catch with 9:18 remaining in the first half.
Renner completed 14 of 29 passes for 218 yards with two touchdowns and one interception. Morris had 11 carries for 54 yards and one touchdown.
Lee completed 7 of 12 passes for 104 yards, including a 21-yard touchdown pass to Darren Waller in the second quarter. Lee had 24 carries for 55 yards and a touchdown.
Steady rain throughout the game may have contributed to a key lost fumble by Lee late in the first quarter. Darius Lipford recovered for North Carolina at the Tar Heels' 46.
Renner led a quick six-play touchdown drive capped by Ebron's 19-yard scoring catch. Ebron pulled the ball in with one hand before falling back in the end zone, giving the Tar Heels a 13-0 lead.
Georgia Tech had trouble holding the ball even as it scored its first touchdown. Sims, hit by Tre Boston, was losing the ball as he crossed the goal line from the 1 early in the second quarter.
A video review confirmed the on-field ruling that Sims crossed the goal line before losing the ball.
Georgia Tech lost only one of four fumbles. North Carolina did not have a fumble.
North Carolina announced before the game tight end Jack Tabb was suspended for two games for an undisclosed violation of team rules. Tabb, listed as a co-starter with Eric Ebron, also will miss next week's home game against East Carolina.
Georgia Tech lost three starters from its defense to injuries during the game. Linebacker Quayshawn Nealy and safety Chris Melton left in the first half and did not return. Another starting safety, Jamal Golden, was taken to the locker room in the third quarter.