The Aggies, who lost the tournament opener to Western Michigan Friday, went on a 10-0 run that put them up 64-50 with 3:36 left to play.
Mullings backcourt mate, D.K. Eldridge, added 14 points for New Mexico State (1-1), and center Sim Bhullar added 12 points and eight rebounds.
The Tigers (0-2) trailed by just four, 54-50, with under 7:00 to play, but turned cold from the floor while New Mexico State put the game away.
Patrick Miller led all scorers with a career-high 30 points for Tennessee State (0-2), connecting on 12 of 22 shots from the field.
The four-team, round-robin tournament wraps up Monday, with Tennessee State playing Western Michigan and the Aggies playing Hawaii.