Nesbitt's score came after Jimmy Newman booted a 34-yard field goal on Wake Forest's opening possession of the extra session that had put the Demon Deacons up 27-24.
Nesbitt finished with 54 yards rushing and two scores but had an off-day passing, completing just 4-of-14 for 51 yards and an interception.
Jonathan Dwyer had a game-high 189 yards and one touchdown on 23 carries. Preston Lyons added a rushing TD in the seventh straight win for the Yellow Jackets (9-1, 6-1 ACC).
Wake Forest (4-6, 2-4) was led by Riley Skinner, who was 26-of-40 for 263 yards and two touchdowns.
Marshall Williams had 111 yards on eight catches and Devon Brown had seven catches for 62 yards and two TDs.