The Huskies, who entered the game ranked 21st in the AP poll and 23rd in the ESPN/USA Today coaches poll, trailed by as much as 10 in the second half but battled back, taking a 60-59 lead on a trio of free throws by Ryan Boatright with 2:23 left in the game.
But sophomore point guard Hugh Greenwood answered with a trey of his own to spark UNM's final run. The Lobos hit all four of their free throws in the final 39 seconds as part of a school record 21 of 21 performance from the charity stripe.
"I like the fight in this team," said UNM head coach Steve Alford. "I think we won this championship at the free-throw line. Obviously, it (free-throw shooting) is emphasized. But the guys have to get there first and then make them. We're making them. We set a school record tonight."
Greenwood added 12 points and seven rebounds for New Mexico (4-0). Tony Snell added 11 points and Alex Kirk scored 10 points and pulled in four rebounds. Cam Bairstow came off the bench to add eight points and six rebounds.
Shabazz Napier led Connecticut (4-1) with 23 points, including 13 straight Husky points during one second-half stretch. Boatright added 12 points and Omar Calhoun 10.
The two teams battled back and forth in the first half as neither team was able to find its shooting stroke. New Mexico shot just 8 of 24 in the half (33 %), but was flawless at the free-throw line, shooting 11 of11. UConn held and early 6-2 lead then led 23-17 the Lobos launched a 10-2 run to grab a 27-25 lead. Snell hit a 3-pointer to end the first-half as UNM took a 30-27 lead into halftime.
The Lobos opened the second half on a 9-2 run, extending the lead to 39-29 but Napier led UConn back and the Huskies took their only lead of the game at 60-59 before UNM rallied for the win.
"Any time, before Thanksgiving, you can have three wins away from your place, that's huge," Alford said. "It was great. We beat a national ranked team in the third game in four days. We showed some of our depth and I like how we guarded. We know we have a lot of weaknesses and we have to get home and work on those weaknesses over the holidays.
"But this win makes the long trip home tomorrow (Tuesday) very, very nice," said Alford.
New Mexico outrebounded UConn 30-20 and the Lobos bench outscored the Huskie reserves 18-4. The Lobos reserves – Bairstow, Adams, Jamal Fenton, Nick Banyard and Cleveland Thomas – combined to shoot 5 of 9 from the field, 8 of 8 on free throws and combined for 10 rebounds, 3 assists and 2 steals in 57 minutes of play. Fenton scored UNM's first four points of the game.