Senior center Chris Jackson grabbed 19 points and 13 rebounds while fellow senior Brandon Mason had 15 points, eight rebounds, four assists and a steal.
Chris Davis led North Texas with 18 points before fouling out.
The Aggies finished the regular season 19-8 and 9-6 in the Sun Belt Conference and finished 12-2 at home this season.
North Texas finished the regular season 7-20 and 2-13 in league play.
The two teams were tied at 37 at the half and the two teams stayed within four points of each for the first seven minutes of the second half.
But the Aggies put together an 8-0 scoring run and held the Mean Green scoreless for nearly four minutes.
North Texas cut the Aggies' lead to three on a jumper by Davis with 13:14 left in the game. It would be the last North Texas point until Jerome Rogers made a layup with 9:35 left in that game.
During that stretch Mason hit a jumper and Moore scored six points, four from the field and two from the free throw line.
The Aggies stretched their lead to as many as 14, 66-52, and North Texas would get no closer than five the rest of the way.
New Mexico State dominated the Mean Green at the free throw line, hitting 29 of 37 shots while North Texas made 12 of 16. Moore hit 13 of 16 of his shots from the stripe. The first was as equal in the boxscore statistics as it was on the scoreboard as the two teams went to the locker room tied at 37.
There were 15 lead changes and seven ties in the first 20 minutes and neither team led by more than six points.
The Aggies shot 52 percent from the floor overall and North Texas countered at 50 percent. The Mean Green did have an advantage from 3-point territory, hitting 4-of-6 3-points shots while the Aggies missed all five of their attempts. NMSU made up for its deficiency behind the 3-point arc by hitting 13 of 16 free throws while North Texas was just 4-6.
Mason and Jackson combined to score 19 points, grab eight rebounds and hit seven of eight shots from the floor.
The Aggies will play the winner of the North Texas - Arkansas-Little Rock in the second round of the Sun Belt Conference Tournament next Sunday night at 7:00 p.m.