Had North Carolina (24-9) lost, it would've been the first time since 1979 the Tar Heels and rival Duke lost on the same day of the tournament.
The Blue Devils fell earlier to 14th-seeded Mercer, and the Friars nearly handed North Carolina a similar stunner.
Marcus Paige led North Carolina with 19 points.
North Carolina tipped off loathe to wind up as another NCAA blue blood sent packing by a smaller school reveling in a rare tournament berth.
Tar Heels fans didn't seem worried: when Duke's 78-71 loss flashed on the scoreboard, a burst of applause erupted.
But they'd wind up squirming in their seats worried about suffering a similar fate.
The Friars, who haven't won in the tournament since 1997, squeezed everything out of their six-man rotation to give talent-rich North Carolina all it could handle. Each time the Tar Heels flexed their unmatchable athleticism - forward J.P. Tokoto's spinning dunk after swiping a midcourt pass got everyone gasping - Providence answered.
Cotton made sure of it.
Saving the performance of his career for his final game at Providence, Cotton was 13 of 23 from the floor and had eight assists. But there was nothing on his face but anguish after corralling a missed McAdoo free throw with less than 2 seconds left, only to bumble the ball off his knee and out of bounds.
McAdoo finished with 16 points and 10 rebounds and Brice Johnson also scored 16 for the Tar Heels.
Ladontae Henton was Cotton's sidekick, finishing with 16 points and 11 rebounds. Tyler Harris added 13 for the Friars (23-12), who were a bubble team before winning the Big East tournament.
Providence trailed just 39-36 at halftime, and with 10 minutes left, a nifty one-handed turnaround by Cotton pulled the Friars within a basket. The senior never came out for a breather, playing every possible minute for the 16th time in 19 games.
Two possessions later, Providence's ironman struck again - this time to put the Friars up 60-58, their first lead since halftime.
Cotton - the smallest guy on the floor at 6-1 - made a 3-pointer to push Providence's lead and then roared at midcourt, while North Carolina trudged back to the bench looking baffled.
But Paige brought the Tar Heels back, hitting a 3-pointer with 1:06 left to tie the game at 77.