The Rebels (21-12) trailed until Moody led a 15-2 run midway through the second half. He hit a late 3-pointer that helped finish off the tournament's first big comeback.
Ole Miss goes to Jacksonville, Florida, to play sixth-seeded Xavier on Thursday afternoon in the East Region.
BYU (25-10) pulled off the biggest comeback in NCAA Tournament history in Dayton three years ago, rallying from a 25-point first-half deficit to a 78-72 win over Iona. This time, the Cougars couldn't hold the big lead.
Tyler Haws, BYU's all-time leading scorer, had 33 points.