N.C. State guard Trevor Lacey made two foul shots with 1.7 seconds left despite trying to miss the second one. Paige answered with two more free throws.
Forward Kennedy Meeks scored 15 points and sophomore forward Isaiah Hicks added a career-best 12 points for the Tar Heels (13-4, 3-1 ACC). North Carolina forward Brice Johnson provided 10 points before fouling out at the 5:10 mark.
For N.C. State (12-5, 3-2), guard Ralston Turner scored 20 points, Lacey had 19, and forward Kyle Washington scored 17 points.
Paige's 3-pointer with the shot clock winding down pushed North Carolina's lead to 71-60 with 4:22 left. Still, he didn't need the heroics of last year when he made the game-winning shot in overtime on this same stage.
Turner's four-point play drew the Wolfpack within 73-68 with 2:40 remaining. His 3-pointer on the next possession closed the gap to 74-71.
N.C. State got the ball back with 44 seconds left on a shot-clock violation, but Turner missed a 3-pointer this time.
Paige sank two foul shots at the other end. After Turner missed, the Wolfpack retrieved the ball and Lacey made his first 3-pointer with 14 seconds to go to close within 76-74.
Tar Heels forward J.P. Tokoto made the first of two free-throw attempts with 11.5 seconds left. North Carolina sent N.C. State guard Cat Barber to the foul line with 3.9 seconds remaining and he made both before Britt's foul shots.
The defensive work by Tokoto on Lacey, who was 2 for 10 from the field at one juncture, was key for much of the game. Lacey went to work at the free-throw line, where he picked up 10 points in the second half.
Washington scored seven points in the first four minutes of the second half to help prevent the Tar Heels from pulling away until the midway mark of the second half.
North Carolina owned a 62-52 lead with nine minutes to play.
Forward BeeJay Anya, who was one of N.C. State's standouts in Sunday's upset of Duke, fouled out with 6:58 left, having scored two points.
North Carolina held a 32-26 halftime lead, aided by 58.3 percent shooting from the field.
Neither team led by more than three points until the final minute of the half.
The Wolfpack were buoyed by 12 offensive rebounds in the first 20 minutes. That helped make up for 33.3 percent shooting.
Turner scored eight of North Carolina State's first 13 points, but he played only 10 first-half minutes because of two fouls.
Both teams were 2-for-6 on free throws in the first half.