Andrew Smith supplied 13 points and Khyle Marshall chipped in with a double-double of 10 and 11 rebounds for the Bulldogs (3-1).
Butler now advances to face Illinois in Wednesday's tournament final.
The Tar Heels (4-1) were led by P.J. Hairston with 15 points and seven boards.
Marcus Paige and Reggie Bullock also reached double figures with 13 points apiece in the loss.