Paige had back-to-back 3-pointers to get that second run going, as North Carolina turned a nine-point edge into a 62-38 lead with 9:12 left.
Norman Powell scored 15 points for UCLA (4-2), which dropped its second straight. Kevon Looney scored 11 points and Bryce Alford finished with 10 points for the Bruins.
It was a matchup of storied programs. Between them, North Carolina and UCLA have 35 Final Four appearances and 16 national championships - though both saw their chances of returning from the Bahamas with a title vanish with losses in Thursday's quarterfinals.
A shot at fifth place will have to do for North Carolina, which will try to leave Atlantis with a 2-1 mark after it plays either No. 18 Florida or Alabama-Birmingham on Friday night.
Both teams led for exactly 9 minutes, 40 seconds in the first half, suggesting things were fairly even.
It wasn't even close.
UCLA raced out to an 18-11 lead. After that, it was all Carolina. The Tar Heels outscored UCLA by 21 points in the final 13 minutes of the half, their reserves outscoring the Bruins' bench 18-0. Theo Pinson slammed in an offensive rebound just before the buzzer to give North Carolina a 43-29 lead at halftime.
The Bruins' comeback hopes took a hit just six seconds into the second half when Kevon Looney picked up his fourth foul and headed to the bench.
North Carolina: The Tar Heels are now 7-3 against UCLA. ... The 22-point margin is North Carolina's biggest win over a ranked opponent since beating then-No. 13 Michigan State 98-63 on Dec. 3, 2008.
UCLA: Something about playing North Carolina at an in-season tournament doesn't work for the Bruins. Thursday's game was the 17th anniversary of the Tar Heels' 109-68 win over the Bruins at the Great Alaska Shootout. ... UCLA came into the game shooting 39 percent from 3-point range this season. The Bruins were 1 for 14 from beyond the arc Thursday.
North Carolina: No. 18 Florida in fifth-place game Friday.
UCLA: Alabama-Birmingham in seventh-place game Friday.