McAdoo shot 10 of 20 from the field in the first game of the season for both teams. Dexter Strickland added 13 points for the new-look Tar Heels, who improved to 91-12 in openers.
North Carolina overcame 18 turnovers, 1-of-12 shooting from 3-point range and a 9-of-19 mark at the free throw line to win for the 80th time in its last 82 home openers.
"Gardner-Webb has an experienced team, and they made us look bad at times," North Carolina coach Roy Williams said. "I'm disappointed in how we played, but I'm not disappointed in my team. I think it was a good night for us, and I think we learned a lot."
North Carolina got off to a slow start with four new starters, including freshman point guard Marcus Paige, a season after winning the Atlantic Coast Conference regular-season title. The Tar Heels had three turnovers and an airball during a five-possession span early as Gardner-Webb took a 13-12 lead 7 minutes into the game.
But Joel James answered with a putback and a jumper as part of a 6-0 spurt to put the Tar Heels ahead 20-14 midway through the half, and they never trailed again.
McAdoo, who played behind All-ACC big men John Henson and Tyler Zeller a year ago as a freshman, scored 15 points in the first half. He sailed past his previous career scoring high of 17 points early in the second half on a hanging bank shot from inside the right elbow.
"I feel like now I know what I'm capable of doing," McAdoo said. "Last year I was just going out there just trying to find a loose ball here and there and fit in. This year I'm embracing my role."
McAdoo's emergence was only part of the good news for North Carolina.
Strickland and fellow guard Leslie McDonald made successful returns to game action after knee surgery.
Strickland played in his first game since midway through last season, when he tore the anterior cruciate ligament in his right knee at Virginia Tech. He showed no signs of being tentative, coming up with three steals and racing toward the basket aggressively for layups in transition.
"I worked too hard in the summer for there to be any rust," Strickland said. "I'm a senior, so that experience that I have doesn't allow any rust to fall on me. I felt comfortable. I was just glad to be back."
Donta Harper and Max Landis scored 13 points each to lead Gardner-Webb, which dropped to 0-16 against ACC competition. Mike Byron added 10 for the Bulldogs.
North Carolina took its biggest lead at 57-39 midway through the second half. The Bulldogs cut the deficit to 63-54 on a 3-pointer by Isaiah Ivey with 4:55 remaining before the Tar Heels answered with an 8-0 run.
"We just played a little bit better in the second half and stayed with it," Gardner-Webb coach Chris Holtmann said. "I'm proud of our guys for that, but we certainly have a lot to clean up in terms of rebounding the ball better and not turning the ball over if we're going to be a better team."
North Carolina led 38-26 at halftime, pulling away midway through the first half with an 8-0 spurt.
McAdoo scored on a putback dunk and added a turnaround jumper from the left baseline as the Tar Heels turned a three-point advantage into a 30-19 lead with 5 minutes remaining.
The outsized Bulldogs leaned heavily on the 3-point shot, but the long-range jumpers misfired. Gardner-Webb shot 6 of 22 on 3-pointers, including 3 of 14 in the first half.