The Lobos will play top-seeded Alabama in the second round.
No. 4 seed New Mexico (22-12) took its first lead at the 6:37 mark of the first half when A.J. Hardeman banked in a turnaround jumper in the midst of a 10-0 run that put the Lobos up 27-21.
New Mexico, playing its first game without injured senior point guard Dairese Gary, opened the second half with a 6-0 surge to extend its lead to 40-30 with 16:35 left.
"I was a little uneasy going into this one just because it's been a long time since having the little bus directing us to start the game," Lobos coach Steve Alford said of Gary, who had started every game since walking on campus.
Later in the half, Phillip McDonald, who had been 1 for 7 from the field, hit three consecutive 3-pointers in a 9-2 run that extended UNM's lead to 54-41 with 6:41 left.
"Phillip's been a little inconsistent," Alford noted. "He'll be the first to tell you that. We're a lot better when he's making shots, that's for sure."
In the first half, McDonald re-aggravated a right elbow injury that has bothered him all season.
"The one thing Phillip is, is he's tough," Alford said. "I think he really showed some toughness tonight when he didn't shoot the ball well in the first half, then he made huge shots."
Randy Culpepper led the fifth-seeded Miners (25-10) with 23 points, but only one teammate was in double figures.
One key to the victory was New Mexico's ability to control the backboards. The Lobos held a 41-26 rebounding edge, including 12-4 on the offensive end.
"We dominated the glass, which I thought we could," Alford said.
That was an area that concerned UTEP coach Tim Floyd, particularly offensively.
"It's a real weakness with our team," he said. "We had to be one of the poorest offensive rebounding teams in the country. Unless you make every shot, it's a very difficult way to play."
The game had a little extra edge to it because the teams got into a verbal altercation during the morning warmup sessions.
"All I know is they were scheduled from 9:30 to 10:30 and we were scheduled at 10:45," Alford said. "And at 10:55, we still weren't on the floor."
Floyd said the problem was a misunderstanding that got a little heated.
"It was an unfortunate situation," he said. "The Lobos apparently wanted a 2-hour block and gave us a 1-hour block. We felt like our shootaround was interrupted. This was not a home game. This was an NIT championship-level event. And they walked into our shootaround and it became disruptive. That's certainly no excuse on what happened."