Thomas finished with 19 points and 13 rebounds and Bellfield had 15 points for the Rebels (21-7, 9-5 Mountain West).
UNLV missed six consecutive foul shots in the final 8 minutes of regulation but took advantage of a key miss by New Mexico late.
After Gary made just 1-of-2 free throws with 27.2 seconds to put the Lobos up 67-65, Bellfield scored on a layup that forced overtime.
UNLV took a 72-70 lead on Thomas' putback with 2:55 remaining in OT and led the rest of the way.
Andy Katz breaks down the likelihood of Villanova, Syracuse, North Carolina or Oklahoma making a run to the Final Four next season.
Florida State has announced that Xavier Rathan-Mayes will return to the court for his junior season. The 6-foot-4 guard declared for the NBA draft last month but did not hire an agent.
Virginia coach Tony Bennett takes the ACC Fast Break with Dino Gaudio by answering questions like who the best Tony Bennett is and what other sport he'd like to coach.