The Aggies (14-12, 8-4 Western Athletic Conference), who trailed by as many as 11 points in the first half, led by seven, 48-41, with 4:55 left in the game.
Kenyon McNeaill, who led the Bulldogs (11-15, 2-10) with 17 points, hit two free throws and a pair of 3-pointers to give them a 49-48 lead with 36 seconds left.
New Mexico State scored the first seven points of the second half to take its first lead of the game, 33-31, after a layup by B.J. West, a three-point play by Tshilidzi Nephawe and a steal and layup by Laroche.
Louisiana Tech shot just 23.5 percent (4 of 17) in the second half after making 57.9 percent of its shots (11 of 19) in the first.
DeAndre Brown had 13 points for the Bulldogs.