The No. 2 seeded Aggies (23-8) outscored the Bulldogs 11-1 in the first 4 1/2 minutes of the second half to break it open. The Aggies led 70-51 with 4:09 left before Tech closed the gap with some late 3-pointers by guard Trey McDowell.
The 23 wins is the most for New Mexico State since the 1998-99 season, when the Aggies lost to Kentucky in the first round of the NCAA tournament. That was also the last time the Aggies made the tournament.
Despite the win, New Mexico State remains a bubble team heading into Friday's WAC semifinals against Boise State (17-13).
Nelson hit a jumper in the lane, added a layup and connected from 14 feet early in the second half run. Hatila Passos hit a free throw and 7-footer Martin Iti turned a Louisiana Tech turnover into a dunk to put the Aggies up 51-33 with 15:48 left.
Louisiana Tech (10-20) couldn't slow down the Aggies' uptempo, above-the-rim offense and the seventh-seeded Bulldogs couldn't handle New Mexico State's defensive pressure during that decisive stretch.