ALBUQUERQUE — Max Hall ran into the locker room after BYU's exciting but sloppy 31-24 win over New Mexico pumping his fist and celebrating a hard-fought win.

This came moments after half of New Mexico's team shook hands with BYU players and the other half walked off the field in bitter disappointment.

It was that kind of battle here Saturday night.

Hall should celebrate. In perhaps the biggest pressure test of his young career, he delivered in a big road win. He did so just like John Beck in Albuquerque back in 2005 when BYU, under new coach Bronco Mendenhall, was struggling to find itself but mounted key plays to win.

That win defined Beck and his teammates, and they went on to go to a bowl game and build a foundation for an 11-2 mark the next year.

Just like that comeback win in 2005 when a late Lobo turnover proved pivotal, the Cougars came up with a special teams fumble recovery by Chris Bolden late in the fourth quarter on a punt to give BYU its third straight win over New Mexico.

BYU senior captain Matt Allen praised Hall's performance, which included overcoming a first-half interception and a second-half fumble that gave the Lobos a short field.

"Max didn't back down," Allen said. "He never quit. He just kept coming and coming. He showed he had guts out there with them coming at him man-on-man, blitzing on almost every down. This wasn't a pretty game, but it was a tough game and their defense did a great job."

Hall completed 18 of 40 passes for 251 yards and two touchdowns. His 62-yard bomb to Austin Collie is the longest of his career. For the game, facing a tough defense, Hall's pass efficiency rating was 109.21.

But that's just it. He faced a huge challenge with Rocky Long's tough defense. The Lobos kept seven to eight men in the box and had BYU's running plays all sniffed out. They pressured Hall, forcing him to make throws and avoid getting sacked. He got popped several times but also made the Lobos pay — exactly what is required in man coverage.

"Max showed why he is such a great quarterback," said Allen. " He never backed down. I can't tell you how much that means to an offense to have a leader like that, leading the way."

The win lifted the Cougars to 3-2 overall and 2-0 in league play. The Lobos dropped to 3-2 and 0-1 in the league standings.

"I think the players played extremely hard, but we turned the ball over too much," said UNM coach Rocky Long.

"I thought the defense played fairly well, but we got beat a few times in man-to-man coverage. I think we got decent pressure on the quarterback tonight and the secondary played well."

Long told his players: "BYU is no better football team than we are. Make no mistake, they deserved to win the game, but they're no better football team than we are."