Chasson Randle had to cherish the moment. Robbie Lemons may think he's living a dream.
Anthony Brown and Stefan Nastic each added 10 points for Stanford, which proved it belonged in the tournament by winning in its first appearance in six years.
The Cardinal (22-12) faces Kansas in Sunday's third round at 9:15 a.m. (CBS). The second-seeded Jayhawks beat Eastern Kentucky, 80-69.
Randle and Brown each played the full 40 minutes, while Josh Huestis went 36. The two guards also combined for 12 of the team's 35 rebounds and five of the 10 assists.
"We came out energetic and ready to go and we sustained it for most of the game," Randle said. "We knew how big this game was. We definitely had enough confidence to finish out the game."
The Lobos drew within 54-52 with 31 seconds remaining to play in the contest. Lemons toed the foul line seven seconds later and calmly sank a pair of free throws for his only points of the game.
"There is not a player who spends any more time on his game and in the gym," Stanford coach Johnny Dawkins said. "And a walk-on having that commitment for four years, for him to go to the line, you know he had to dream of that moment."
After New Mexico missed a 3-point attempt, Randle added a pair of free throws to put Stanford up, 58-52, with eight seconds left.
Stanford held an early 16-point advantage and then held on after New Mexico rallied to tie it midway through the second half.
Randle hit a 3-pointer to give Stanford the lead again as the Cardinal won its first NCAA game under Dawkins.
"I haven't had the chance to even think about that," Dawkins said. "I have been in this tournament a number of times as a player and coach and the thing you have to do is stay focused on what you're doing. Both of those teams are great, neither one of those teams would be here if they weren't very good at what they do."
Long-range shooting was a key, with Stanford going 8 for 15, with Brown making all three of his attempts, and New Mexico going 4 for 21.
"We didn't want to be happy to just be here, and that is one of the things coach stressed this entire week," Brown said. "There are a lot of teams that come to the tournament and are just happy to be here and they go home the first day."
Dwight Powell, Stanford's second-leading scorer, missed all eight of his shots, fouled out and scored three points.
"You're going to have to win games like this where your best player is not at their best," Dawkins said. "I think he's a young man that will bounce back. He always has."
Stanford hit eight of its first 10 shots and scored 17 straight points, including six from Randle, for a 20-4 lead with 13:23 to go in the first half.
"We got out early, they kept fighting, they kept coming back," Dawkins said. "Guys stepped up and made plays when we really needed them."
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