The victory moved New Mexico into the semifinals of the Mountain West Conference Tournament, where the Lobos will meet either San Diego State or Boise State on Friday.
In the opening two quarterfinal games of the day, Nevada-Las Vegas held off Air Force 72-56 and Colorado State was a 67-61 winner over Fresno State.
New Mexico shot just 40 percent from the field, but the Lobos made 21 from the foul line -- 13 more than did the Cowboys.
Snell scored 15 points and Cameron Bairstow added 14 for the Lobos (27-5). New Mexico had only a six-point lead with 7 minutes remaining, but held Wyoming (19-13) scoreless for a stretch of almost 5 minutes to take control.
UNLV (24-8), which had trouble in its two meetings with Air Force during the regular season, was led by 23 points from Anthony Bennett -- who hit 10-of-14 from the field and grabbed seven rebounds.
Air Force (17-13) lost leading scorer Michael Lyons to a knee injury in the early stages of the game.
Colorado State held on against Fresno State thanks to 18 points from Wes Eikmeier. The Rams (25-7) will meet UNLV in the semifinals on Friday. Those teams split their two meetings this season.