The Lobos, who are out front in the Mountain West Conference, hit 24-of-32 from the foul line and relied on the strong presence in the paint of their 7-0 center.
Kirk hit 8-of-12 from the field, connected on all six of his free throw attempts and grabbed seven rebounds.
Cameron Bairstow had 16 points and Tony Snell added 10 for the Lobos (24-4, 11-2 MWC). New Mexico has a two-game lead over Colorado State in the league race with three games remaining.
San Diego State (20-8, 8-6) was led by Jamaal Franklin with 16, the only member of the Aztecs in double figures.
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