Mandi Moore hit four 3-pointers to spark a 17-6 second-half run, helping the sixth-seeded Lobos rally from a 40-29 halftime deficit.
The victory came before a crowd of 16,151, the largest ever to see a first-round game in the women's NCAA tournament.
Freshman Tamara James led the 11th-seeded Hurricanes (18-13) with 23 points, and Yalonda McCormick had 20.
Moore and Chelsea Grear each scored 18 points for New Mexico (23-8), which advances to play Mississippi State (25-7) in the second round Monday. Mississippi State beat Manhattan 73-47.
New Mexico took control in overtime on five free throws by Adams, Cristal Garcia and Grear. Adams, who had eight blocks, also made a layup and a 14-foot jumper to put the Lobos up 87-79 with 1:36 remaining.
New Mexico and Miami both had a chance to win in regulation. Adams missed three free throws in the final 46 seconds, including two with 8.9 seconds left.
After the second miss, Miami got the ball up the court, but McCormick's off-balance 14-footer with 2 seconds left was an airball.
New Mexico trailed 49-35 with just over 15 minutes left after McCormick scored underneath. New Mexico, which had struggled against the Hurricanes' quickness throughout the first half, suddenly began making shots. And it was Moore who got it started.
With Moore hitting 3s from the top of the key, New Mexico cut the deficit to 55-52 with 11:43 remaining. A 3-pointer by Lauren McLeod gave New Mexico its first lead of the game at 62-61. That came in the midst of an 11-0 run that put the Lobos up 69-61 with 4:44 left.
But Miami battled back to force overtime as James scored 10 points over the final 3:34.
Lady Canes Fall in OT
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