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.
Former Kentucky guard Ed Davender, the only Wildcat with at least 1,500 points and 400 assists, has died. He was 49.
Guard Naz Mitrou-Long, whose 2015-16 season ended in December due to hip problems, has been granted a hardship waiver for the coming season, Iowa State said.
As the Sooners look to life without superstar Buddy Hield and his sidekicks, it's clear their unseasoned players will need to grow up fast.