James Michael McAdoo had 22 points and 10 rebounds and Reggie Bullock added 11 points for the Tar Heels (15-6, 5-3 Atlantic Coast Conference).
They hounded the nation's leading scorer, Erick Green, into his second-worst game of the season and scored on their first nine possessions of overtime to pull away for their fifth win in six games.
Green, who averages 25.5 points, finished with 16 on 7-for-21 shooting while being defended mostly by Dexter Strickland.
Green missed a jumper that would have won it in regulation and was held to fewer than 20 points for just the second time this season.
Jarell Eddie added 15 points for the Hokies (11-10, 2-6). They have lost four straight and 10 of 14 since starting 7-0.
McAdoo put North Carolina ahead to stay with a jumper that made it 59-57 with 3:45 left in overtime. Joey van Zegeren pulled the Hokies within one with a free throw on their next trip downcourt.
That's when Paige took over.
He entered 8-for-39 in the past five games but was 6-for-14 in this one while hitting four of his team's five 3-pointers.
His open 3 from the left wing with 3 minutes left in OT made it 62-58, and he followed that with a jumper from the baseline that made it a six-point game. His three free throws in the final 1:36 helped ice it.
Cadarian Raines finished with 12 points and Robert Brown added 10 for the Hokies, who had a chance to win it in regulation.
Van Zegeren - a 46 percent free-throw shooter - tied it at 55 with two foul shots with 45.8 seconds left, and the Hokies got the ball back when Paige threw the ball away with about 30 seconds left.
Green milked the clock before his pull-up jumper from the wing over Bullock didn't hit anything, and North Carolina rebounded with 1.9 seconds left. Jackson Simmons' full-court pass was tipped out by a Hokie with 0.1 seconds. After a timeout, van Zegeren picked off Paige's inbounds pass in the lane.
North Carolina trailed by eight twice in the second half, but clawed back with a McAdoo-led 19-9 run to take its first lead.
Bullock, who missed his first five 3-pointers, swished an open 3 to make it 42-all with just over 13 minutes left. Brice Johnson then put the Tar Heels up 46-45 on a tip-in with 9½ minutes to go. After McAdoo stretched it to 47-45 on a free throw with 9:01 left, it was a one-possession game throughout the rest of regulation.
The Tar Heels played without injured swingman P.J. Hairston, who suffered a concussion in their last game at Boston College, and his absence was felt on the perimeter. They were 5 of 24 from 3-point range, with Bullock missing seven of his eight.