The Lobos had to fight off their in-state rival down the stretch to remain unbeaten in their 12 games this season.
Duke and Cincinnati also preserved their perfect records Wednesday, staying among major college basketball's unbeaten teams with Syracuse, Illinois Michigan, Wyoming and Arizona.
New Mexico State was within five points when Fenton went to the foul line with 14 seconds remaining. Fenton missed both free throws, but moments later he stole the ball and made a layup to ensure the win. Those were Fenton's only two points of the game.
Tony Snell added 11 points for New Mexico and Hugh Greenwood had 10.
Daniel Mullings (5-6) led the Aggies with 13 points.