Withey provided 16 points and 16 rebounds for the Jayhawks (31-5), who broke open a close game with a second-half surge and advanced to their third straight Sweet 16 appearance.
Kevin Young helped out with 10 points and nine boards for top-seeded Kansas, which will next face fourth-seeded Michigan Friday in the South Regional semifinals.
The Tar Heels (25-11) got 15 points and nine rebounds from P.J. Hairston, and James Michael McAdoo added 11 points and six rebounds.
Celebrity Families of 2014 [PHOTOS]