The Patriots managed to get up a desperation shot at the buzzer but it was far wide and off.
"We found a way to win," said New Mexico head coach Steve Alford. "We made two unbelievable plays down the stretch and now we get a chance to play in the championship."
Snell finished with a game high 27 points on 8 of 12 shooting and 4 of 6 on 3-pointers for New Mexico (3-0). Williams added 14 points and four assists but committed five of UNM's 19 turnovers. Junior forward Cameron Bairstow added 10 points and five rebounds while Alex Kirk came off the bench to score eight points and nine rebounds.
Sherrod Wright paced George Mason (2-2) with 22 points and Johnny Williams and Patrick Holloway added 12 and 11 points respectively.
The two teams were tied 28-28 at halftime after a poor shooting half for both teams but the Patriots warmed up from behind the three-point line and GMU took a 48-41 lead with 11:24 left in the half. The Lobos whittled the lead down to 63-62 on a trey by Alex Kirk with 1:13 left in the game.
But Wright came back and hit a trey and was fouled by Snell and the four-point play gave the Patriots a 67-62 lead. George Mason had a chance to push the lead to seven after a turnover by Greenwood but missed the front end of a one-and-one. After a Lobos basket, Wright hit a pair of free throws to take the score to 69-64, setting up the final sequence for New Mexico.
"This was a great win," said Alford. "It was a very good team we beat in George Mason. It was the best they shot the ball all year. We didn't play very good basketball, but we are 3-and-0.
The Lobos, who finished 22 of 55 shooting (44%) and 9 of 18 on treys, made eight of their last nine FGs, including their last five 3-point attempts. The Patriots shot 41% for 24 of 58, 11 of 23 on three-pointers. George Mason outrebounded UNM 31 to 27.