The Lobos opened their Mountain West Conference campaign by playing their first game of 2013.
New Mexico fell behind 58-56 when Justin Hawkins made a 3-pointer with 3:30 to play, but the Lobos then fought back behind a 3-pointer and a pair of free throws from Williams.
Alex Kirk led New Mexico (14-2) with 23 points and eight rebounds. Tony Snell contributed 13 points while Williams had 11.
UNLV, which had won its previous two games, was paced by Khem Birch and Anthony Bennett with 12 points each.