Paige got 21 of his points in the second half as the Tar Heels (7-2) notched a third win against a ranked opponent this season after similar knockoffs of defending national champs Louisville and then-No. 1 Michigan State.
J.P. Tokoto provided 15 points for up-and-down North Carolina, which has also suffered unexpected defeats at the hands of Belmont and Alabama-Birmingham.
The Wildcats (8-3) were plagued by 18 turnovers and committed 31 fouls.
Aaron Harrison put in 20 points and twin brother Andrew provided 17 with seven assists.
James Young scored 16 points for Kentucky.