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.
Maryland point guard Melo Trimble, considered a lock to leave the program before struggling in the second half last season, has withdrawn from the NBA draft and will return for his junior season.
Louisville's Chinanu Onuaku, who recently underwent a medical procedure to correct a heart rhythm issue detected during the combine, will keep his name in the NBA draft pool.
Andrew White III will return to the Nebraska men's basketball team next season after removing his name from the NBA draft.