Strickland netted 16 points while P.J. Hairston provided 15 and four steals as the Tarheels (10-3) logged their fifth win six contests.
James Michael McAdoo (13 points, nine rebounds), Marcus Paige and Brice Johnson (12 points each) helped balance the scoring for North Carolina.
Anthony Bennett had 15 points and 13 rebounds for the Runnin' Rebels (11-2), who had a nine-game winning streak snapped. Katin Reinhardt and Anthony Marshall each scored 15 points for UNLV.