Cameron Bairstow had 14 points and 10 rebounds for the Lobos (22-5, 13-3 Mountain West) while Alex Kirk added 13 points, 11 rebounds and five assists.
Utah State led 47-39 with 11:29 left after Preston Medlin hit a 3-pointer and converted a three-point play.
But Neal started the long run with a 3-pointer and Kirk scored six straight points near the end the surge that left New Mexico holding a 62-52 lead.
The Lobos controlled the glass, holding a 46-30 edge, including 12-6 on the offensive end.
Medlin scored 19 to lead the Aggies (15-13, 5-10).
The Lobos had to shrug off a sluggish first half, trailing 27-26 at the break, despite shooting better from the field and owning the glass 21-13.
New Mexico did take 19-12 lead after a 12-2 run midway through the first half, but the Aggies immediately responded with an 11-0 run to go up 23-19.
The Lobos controlled the glass, holding a 46-30 edge, including 12-6 on the offensive end. And New Mexico turned up the defensive pressure in the second half, holding the Aggies to 36.4 percent (12 for 33), although they did make 5 of 10 3-pointers.
The Lobos did struggle from the line, finishing 11 of 21, but Utah State only made 6 of 12 foul shots.