BOONE, N.C. -- Drake Maye is looking like the real deal.

North Carolina's redshirt freshman quarterback continued his torrid start to the season, throwing for 352 yards and combining for five touchdowns as the Tar Heels outlasted Appalachian State 63-61 on Saturday -- despite surrendering 40 points to the Mountaineers in a wild fourth quarter.

Maye, the younger brother of former Tar Heels basketball star Luke Maye, has thrown a school-record nine touchdown passes in two career starts. He also ran for a score against the Mountaineers.

"He's a special young guy," Tar Heels coach Mack Brown said. "He's a great young quarterback who is only going to get better."

Sixth-year quarterback Chase Brice threw for 376 yards and a school-record six touchdowns -- four of those in the fourth quarter -- for Appalachian State (0-1).

The Tar Heels (2-0) won despite squandering a 20-point fourth-quarter lead and allowing the Mountaineers to gain 664 yards and score nine touchdowns on offense.

But that didn't dampen Brown's enthusiasm.

"You take a win and go," Brown said. "We were underdogs and hadn't won a road game all of last year, so anybody who thinks I'm going to be mad or disappointed over this one doesn't understand coaching. I'm excited to win against a really good team on the road."

The two teams combined for 62 points and 504 yards in the fourth quarter alone. It was one point shy of the most ever in the fourth quarter of an FBS game (Navy vs. North Texas in 2007).

Appalachian State coach Shawn Clark said he was thrilled with the fight his team showed in the fourth quarter.

"We were down 20, and our guys never quit,'' Clark said. "We're going to have a helluva football team. Our guys are hurt, and we're disappointed, but not discouraged. The future is bright at Appalachian State.''

The Tar Heels fell behind 21-7 before rattling off 34 straight points and silencing a record crowd of 40,168 at Kidd Brewer Stadium. Maye threw three TD passes in the first half, including a 10-yard TD strike to Nesbit to give the Tar Heels a 28-21 lead with one second left.

Maye made it 28 straight unanswered points for UNC with a 12-yard touchdown run to start the second half, receiving congrats from former Tar Heels and current Washington Commanders quarterback Sam Howell in the end zone after tiptoeing the sideline.

North Carolina seemed in control, leading 41-21 after the third quarter, but the Mountaineers climbed back into the game behind Brice, who led six TD drives in the final quarter.

Maye showed poise beyond his years in his first road start.

With the game tied at 49, he beat an all-out blitz by lofting a pass over the middle to D.J. Jones for a 42-yard touchdown to give North Carolina the lead with 2:50 left.

"They were bringing the house a couple times trying to hit up a young quarterback," Maye said. "But they forgot about D.J., who slipped out in the seam. He was wide open and I got power driven into the ground. I tried to float him up one and he took care of the rest."

But the game was far from over.

Brice responded with his fifth TD pass of the game, a 28-yard strike to Deshaun Davis with 31 seconds left. The Mountaineers went for the 2-point conversion -- and the win -- but Brice's pass sailed just over a backpedaling Davis' head.

"I had made my mind up early that we were going for two and the win,'' Clark said. "We're not going for second place at Appalachian State.''

The UNC fans celebrated an apparent win.

But when UNC's Bryson Nesbit returned the ensuing onside kick for a 43-yard touchdown -- rather than simply getting down -- it gave the Mountaineers yet another chance to tie the game trailing 63-55.

"Our coaches were yelling, 'No, get down,'" Brown said.

Sure enough, Brice found Kaedin Robinson for a 26-yard TD strike with nine seconds left to cut the lead to 63-61.

The Mountaineers went for 2 but Brice was stopped short of the end zone.

It was the most points ever scored in a UNC game since the school started football in 1888.

The Tar Heels accomplished the feat playing without standout wide receiver Josh Downs, who sat out with a lower body injury.

Downs, arguably the team's best player, had nine catches for 78 yards and two touchdowns in UNC's win over Florida A&M and led the ACC with 101 catches last season for 1,335 yards and eight TDs.

Brown said it's unclear how long Downs will be out.

The Associated Press contributed to this story.