Watson's six TDs tied the ACC record and only Tajh Boyd has thrown for more yards in a game for Clemson.
North Carolina (2-2, 0-1) gave up 528 yards, and has allowed its opponent to gain more than 500 yards in the past three games.
Mike Williams had six catches for 122 yards and two touchdowns for Clemson, which has scored 49 or more points in five of its last 10 ACC games.
Watson was the first true freshman to start for Clemson in 20 years. On Watson's second play he threw a 74-yard touchdown pass to a wide open Germone Hopper.
Watson also had a 50-yard TD pass to Hopper in the second quarter, waiting in the pocket until the last moment to drop the pass right into the receiver's hands. Clemson gained 218 yards in the first half, with Watson's two long passes accounting for more than half that total.
In the second half, Watson had two 33-yard touchdown passes and a 24-yard scoring throw before tight end Jordan Leggett jumped high in the end zone to pull in the freshman's record-breaking TD pass.
Clemson needed Watson's passing because the Tigers gained only 71 yards on the ground.
Ammon Lakip hit a 27-yard and a 45-yard field goal.
The Tar Heels had 15 penalties, one off the school record, for 130 yards, which was 20 yards away from their worst game.
Marquise Williams was 24-of-38 for 345 yards for North Carolina and threw to 13 different receivers. Elijah Hood ran 13 times for 71 yards.