Senior Leslie McDonald added a season-high 21 points for the Tar Heels (19-7, 9-4 Atlantic Coast Conference), who rallied from 11 down in the second half to snap a two-game home losing streak to the Blue Devils (21-6, 10-4).
It was by far North Carolina's most impressive win during the run that has helped the Tar Heels dig out from an 0-3 ACC start.
When it was over, UNC students and fans stormed to midcourt to celebrate a win that was came eight days later than they had hoped due to a winter storm that forced the game's postponement last week.
The Tar Heels shot 47 percent and even made their last 10 free throws in the final 6 minutes after a disastrous start at the line, providing a rousing finish befitting the long-running rivalry.
Jabari Parker and Quinn Cook both scored 17 points to lead Duke, which led 51-40 with about 15 minutes left before going ice cold from the field. The Blue Devils missed 13 straight shots and went scoreless for 6 minutes at one point, helping the Tar Heels climb their way back into the game.
Duke shot 36 percent (11 for 31) after halftime and finished 5 for 22 from 3-point range for the game.
After being hounded throughout the first half by Duke defenders Cook and Rasheed Sulaimon, Paige - who has made a habit out of big second-half performances this season - finally scored about 3½ minutes into the second half.
But he got stronger down the stretch.
After knocking down a 3-pointer, Paige came up with a stepback jumper over Rodney Hood with about 2 minutes left to push North Carolina's lead to 66-62. Then, after two free throws from Parker, Paige drove by Hood into the paint and hit a scooping layup through the heart of Duke's defense to answer and keep it a two-possession game.
After Sulaimon missed a 3 on the ensuing possession, freshman Nate Britt followed with two free throws that pushed the lead to 68-62 with 46.2 seconds left and soon had the rowdy home crowd inching closer to the court to celebrate at the horn.