Bandja Sy added 16 points and 10 rebounds for the Aggies (8-8, 2-2 Western Athletic), who shot 54 percent from the floor and outrebounded the Bobcats 36-25.
Bhullar, a freshman, hit all nine of his shots to post the second 20-point game of his career.
Texas State (4-12, 0-4) got 17 points from Joel Wright and 15 from Deonte Jones.
New Mexico State used a 12-2 run to start the second half to take a 49-39 lead, and never trailed the rest of the way. Mullings started the spurt with a layup and a dunk, and Bhullar closed it with a three-point play and a layup.
Texas State got within 68-65 on a 3-pointer by Matt Staff with 4:13 remaining, but scored only two more points the rest of the way.