Rodney Hood added 24 points to help the Blue Devils (24-7, 13-5) end the Tar Heels' 12-game winning streak and clinch the No. 3 seed in the Atlantic Coast Conference tournament.
Duke never trailed, shot 51 percent — 57 percent in the second half — and dominated the ACC's best team on the glass, outrebounding North Carolina 34-20.
They shot nearly 60 percent but couldn't overcome their disadvantage on the glass and are locked into the No. 4 seed in the league tournament.
Leslie McDonald added 12 points for North Carolina, which was denied its fourth win over a top-five team, but briefly made things tense in the final minutes when Paige converted a four-point play to make it 81-73 with 2:50 left.
But the Tar Heels' point guard missed 3s on the next two possessions — with Parker blocking the second of those with 2½ minutes left.
Cook finished with 11 points and Rasheed Sulaimon added 10.
In what might have been his final game at Cameron Indoor Stadium, Parker put on quite a show.
He hit 10 of his 17 shots, cracked his previous high of 29 points set last month at Boston College and showed off all the skills that have him as a likely high NBA draft pick — should he decide to forego his final three seasons of college eligibility and turn pro.
Parker set the tone early by converting repeatedly around the rim, and he hit two of his four attempts from 3-point range — including one from the corner that gave Duke its largest lead, 74-55, with 8½ minutes left.
When those 3s are falling, the Blue Devils are tough to beat.
When they're not, Duke is usually in trouble.
The Blue Devils were only 5 of 22 from long range in their 74-66 loss in Chapel Hill. They made just 6 of 27 from beyond the arc in a 10-point loss at Wake Forest on Wednesday night.
In this one, Duke missed 12 of its first 14 3-pointers and held a tenuous 47-39 lead when pesky senior guard Tyler Thornton picked up his fourth foul with 17:11 left.
Cook came on to replace him and immediately hit a straightaway 3 that started the Blue Devils' big burst. Andre Dawkins followed with another one from the corner to help the Blue Devils open up a 53-41 lead.
Parker then added a jumper and two free throws before Cook hit and up-and-under layup. And Hood then followed that with a 3 with 14 minutes left to give Duke its largest lead to that point, 62-46.
That shot whipped an already amped-up Cameron crowd — which included Dallas Cowboys quarterback, and apparent Blue Devils fan, Tony Romo cheering enthusiastically from behind the scorers' table — into an absolute frenzy.
There were plenty of famous faces in the crowd for the latest renewal of college basketball's fiercest rivalry: NFL Commissioner Roger Goodell — wearing a Duke sweater — watched from one baseline, while former Oklahoma coaches Barry Switzer and Billy Tubbs sat on the other one.
And Hood and Parker kept them entertained all night.
Those two clicked right from the opening tip — Parker scored 16 points in the first half, and helped the Blue Devils open up a 17-4 lead about 7 minutes in with a drive on Paige.
The Tar Heels — who had as many turnovers (six) as points in the opening 7 minutes — settled themselves down and clawed back in it, with Paige's jumper in the final seconds of the half pulling UNC to 40-37.
But that was as close as they could get.