Trailing by three, the No. 2-seeded Cougars watched as Michael Loyd Jr.'s floater missed with 14. 7 seconds left and Willis hit all his free throws in the closing seconds to seal it.
Playing on their home floor, the No. 3-seeded Rebels grabbed a seven-point halftime lead, led by as many as 11, and for the game shot 55.6 percent from the field. Last month, they beat BYU here by 14 and played with confidence.
More importantly, UNLV added another win against a ranked team in collecting its 25th victory overall.
BYU, meanwhile, hopes to earn its 30th win in the NCAA tournament.