Kevin Durant led all scorers with 27 points (6-of-13 FG), including 15-of-16 foul shots and eight rebounds.
"Every time I went to the line, I had the mindset that I wanted to go up a couple of more points," Durant said. "And I hit 'em."
D.J. Augustin added 19 points (6-of-12 FG) and seven assists. A.J. Abrams contributed 16 points (6-of-13 FG, including 2-of-7 threes). Damion James got into early foul trouble, but Connor Atchley provided seven bench points, eight boards and two blocks.
Texas held NMSU to 39 percent (25-of-64) from the field, including 7-of-25 (28 percent) from three-point range.
"We wanted to pack our defense back in there and force perimeter shots," Texas coach Rick Barnes said during the post-game press conference. "We got great play from a lot of different guys tonight. It was hard fought."
The Horns started off chilly but eventually shot 48 percent (25-of-52 FG), including four of 16 from outside the arc. The taller Aggies controlled the boards, 34-30. But Texas enjoyed a sizeable advantage at the free throw line, connecting on 25-of-26 attempts (96 percent). The Aggies went to the charity stripe just 12 times, hitting 10.
The old adage is that the hardest NCAA Tournament game to win is the first one. The Aggies staked an early 24-19 lead after Texas opened 7-of-24 from the floor. Augustin's trey launched a 12-3 run, including a pull-up jumper and a three-ball from Abrams, to spot the Horns a 33-30 lead at the break.
"I thought we were a little bit jumpy to start with," Barnes said. "You kind of expect that this time of year. The way we ended the half offensively, I thought we'd come out the second half and continue that."
Damion James picked up his third personal 30 seconds into the second period and took a seat. NMSU coach Reggie Theus was whistled for a technical with 15:52 left and Texas leading 40-33. Abrams sank both foul shots before Connor Atchley drained one from outside the arc as part of a 12-0 run. The Aggies connected on consecutive treys to trim the lead, 47-39. The pace picked-up considerably with both teams trading buckets. Eliajh Ingram's third trey pulled NMSU within 53-50 after James was whistled for his fourth.
A pair of Fred Pete foul shots made it a one-point game at the 8:31 mark before Durant's baseline jumper, his first FG of the second period, made it a 57-54 ballgame.
"They did a great job of denying me the ball," Durant said. "When I got the ball in the post, they sent two or three guys at me. I just gave the ball up to my teammates and they made plays, as well. When I got to the free throw line, I hit my free throws."
The Aggies continued to control the offensive boards and frustrated the Horns with their full court press. Gibson's foul shots gave NMSU their first lead of the second period at 58-57 in a game that would see 11 lead-changes.
"We knew they were going to press the whole game," Augustin said. "We were prepared for that. We had to box out and rebound. That was the biggest thing. That's where the game was won."
Texas went back in front, 61-60, after Augustin and Durant hit four shots, but it was short-lived as Hatila Pasos answered with a slam. James snagged a critical rebound and followed with a bank-shot at the opposite end. Durant hit four foul shots as Texas extended its lead, 69-62, with 3:32 left. Augustin's driving lay-up made it a 71-64 contest.
It was a five-point game with two minutes left, but Durant took a charge as Tyrone Nelson fouled out with four points. Justin Mason's clutch free throws made it a three-possession game, 73-66, with 1:12 left. Two more Durant FTS put this game on ice.
The Horns are now 25-9 on the season.