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 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.
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.
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 as they tried to beat North Carolina for the first time in five tries, but the long-range jumpers misfired. Gardner-Webb shot 6 of 22 on 3-pointers, including 3 of 14 in the first half.
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.