Hayden Graham had nine points and six rebounds for Air Force (10-12, 3-8 Mountain West).
Air Force led 28-26 at halftime, but New Mexico took a lead with 16:36 left in the game and held it until the 3-minute mark.
New Mexico led by five, 49-44, with 6:40 remaining, their largest lead of the game, but Air Force scored the last nine points of the game - seven from Olesinski. Trevor Lyons hit two free throws with 36 seconds left to seal it.
New Mexico only hit two field goals in the final 10 minutes.