The Wildcats (5-2) withstood an 8-0 Aggies run to open the second half, and built a 10-point lead with a 14-2 run midway through the half.
Wendell McKines had 28 points and 10 rebounds for the Aggies (5-2), who came back late and trimmed the lead to 79-76 with 1:04 to play.
Arizona guard Kyle Fogg missed the front end of a one-and-one with 29.8 seconds left, but New Mexico State couldn't grab the rebound. Fogg kept the ball alive and flipped it to Jordin Mayes, who was fouled and made two free throws with 21.6 left to push the lead to 81-76.
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Purdue coach Matt Painter says players haven't used the fifth-year graduate transfer rule for its true intent.
The 2017 recruiting class is short on point guards, with Trevon Duval leading only eight prospects from the ESPN 60 who are still available.
The dust has settled after players made their NBA draft decisions. Which college teams won? Which lost? Well, Villanova is pretty happy. USC, meanwhile, might not be as thrilled.