The Lobos (20-12) will host a quarterfinal game Wednesday against either Alabama or Alabama-Birmingham. The two teams will play Sunday in Tuscaloosa, Ala.
At the Pit Saturday night, the Lobos were down 58-55 when Molly McKinnon hit a 3-pointer with 8:29 left and ignited a 20-4 New Mexico run to finish the game.
Arizona (20-12), which has been plagued all season with injuries, played the game with just eight players.
The Wildcats "are athletic, quick and they have size," UNM coach Don Flanagan said. "But the only thing they don't have is depth. We felt that would be a problem for them. I think they got tired late in the game."
Lobo forward Chelsea Grear posted a career-high and team-high 18 points to lead New Mexico. Center Jordan Adams scored 17 points and grabbed 11 rebounds.
Veranda James led the Wildcats with 19 points and nine rebounds.