Paige finished with 17 points for the Tar Heels (8-3), who needed extra time but bounced back from Wednesday's home loss to Texas.
J.P. Tokoto provided 22 points, 11 rebounds, five steals and four blocks and James Michael McAdoo scored 19 points.
North Carolina won in its first game after it was announced suspended junior guard P.J. Hairston would not be reinstated this season due to eligibility issues.
Brian Sullivan led the Wildcats (4-8) with a career-high 33 points, including seven 3-pointers.
His potential game-winning trey bounced off the rim at the buzzer in regulation.
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