The Lobos took the lead in the Mountain West Conference, a league that has put both San Diego State and Nevada-Las Vegas in the national rankings this season.
It was New Mexico's sixth straight victory and came after the Lobos had lost at home to San Diego State by five points.
Williams finished with five field goals from beyond the arc and scored 21 points. Drew Gordon added 17 points and 17 rebounds for the Lobos (21-4, 7-2 MWC).
New Mexico broke open a tie game with its decisive run that gave the Lobos a 51-38 lead with 14:34 to play. San Diego State came no closer than six the rest of the way.
Jamaal Franklin led the Aztecs with 16 points. After opening the season with an 18-2 record, San Diego State (20-5, 6-3) has suffered a 17-point loss to Colorado State, won close games against Boise State and TCU, dropped a two-point decision to UNLV and has now lost to New Mexico.