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.
Maryland point guard Melo Trimble, considered a lock to leave the program before struggling in the second half last season, has withdrawn from the NBA draft and will return for his junior season.
Louisville's Chinanu Onuaku, who recently underwent a medical procedure to correct a heart rhythm issue detected during the combine, will keep his name in the NBA draft pool.
Andrew White III will return to the Nebraska men's basketball team next season after removing his name from the NBA draft.