Kirk put in 15 points and grabbed nine rebounds while Cameron Bairstow supplied 13 and nine as the Lobos (25-4, 12-2 MWC) won their fifth straight.
Tony Snell helped out with nine points for New Mexico, which logged its eighth victory in nine contests overall.
The Cowboys (18-11, 4-11) were led by Riley Grabau with 14 points.
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