J.P. Tokoto posted career-highs of 22 points and 11 rebounds to lead North Carolina, which needed two free throws from Paige with 29.3 seconds left to force the extra session. The Tar Heels dominated the extra period, with Paige scoring in the lane to open the overtime and hitting his only 3-pointer of the game moments later to put UNC in control.
Brian Sullivan had career-highs of 33 points and seven 3-pointers for the Wildcats (4-8), who shot just 2-for-10 in overtime to fade late.
Sullivan had a chance to win it in regulation after Paige's tying free throws but missed a contested 3 over Nate Britt just before the horn. The Tar Heels took over from there, with Paige assisting on Britt's jumper early in the overtime and hitting two free throws before knocking down the 3 that pushed UNC to an 88-80 lead.
The Tar Heels, who rank as one of the nation's worst free-throw shooting teams, then secured the win with an unusually steady performance at the line. North Carolina missed 12 free throws in regulation but went 11-for-12 in overtime to stay in control.
The game followed an eventful week for the Tar Heels, starting with last weekend's tough-it-out win against then-No. 11 Kentucky. Four days later, the NCAA cleared senior Leslie McDonald - who had missed the first nine games due to NCAA eligibility concerns - hours before tipoff of an 86-83 home loss to Texas in a performance that left coach Roy Williams so angry that he scheduled a 5 a.m. practice the next day.
Then, on Friday, the school said it wouldn't seek reinstatement from the NCAA for Hairston after the junior committed several rule violations. Hairston hadn't played all year while the school and NCAA worked to resolve eligibility questions focused largely on the use of cars linked to a felon and party promoter earlier this year.
Hairston practiced with the team once again after Friday's announcement, then was back on the bench Saturday to support his teammates again.
North Carolina had beaten highly ranked Michigan State, Kentucky and Louisville without Hairston and McDonald while the school and NCAA worked to determine their statuses. But the Tar Heels had also lost at home to Belmont and on the road at UAB, then nearly added another surprising loss to that list Saturday.
Davidson shot 46 percent and hit nine 3-pointers. Sullivan had made just 5 of 28 3-pointers in his last four games before going 7-for-14 against the Tar Heels.