New Mexico allowed the Falcons (14-16) to wind down the shot clock with a five-point lead in the final minute and Trevor Lyons' 18-foot jumper with 38 seconds left gave Air Force a 66-59 lead. The Academy held on from there to advance to a quarterfinals matchup with top-seeded Boise State on Thursday.
Air Force took control late with a 9-0 run to lead 58-53 on Kocur's 3-pointer with 3:55 left. Lyons finished with 10 points, five assists and five steals.
The Lobos (15-16) led for most of the first half and had a 52-47 advantage on Sam Logwood's 3-pointer with 7:39 left.