Daniel Mullings scored and New Mexico State led 63-62 with 4:31 remaining. Nance scored the next five points to give Wyoming a 67-63 lead with 4:09 to play. The Cowboys then made 11 of 12 free throws, including four from Nance, to seal it.
Ian Baker hit back-to-back 3-pointers in the closing seconds for New Mexico State (3-4). He drained his second trey with 2 seconds left to end the game.
Charles Hankerson Jr. and Josh Adams scored 15 points, and Riley Grabau added 10 points and five assists for Wyoming (6-0).
Mullings scored 21 points, Pascal Siakam had 19 and Remi Barry chipped in 18 for the Aggies.