Demetrius Walker added 14 points for New Mexico (2-0), which saw its 13-point halftime lead whittled down to two, at 58-56, with 35 seconds remaining, after a steal and layup by UIC's Daniel Barnes.
But the Lobos hit their final eight foul shots down the stretch to hold off the upstart Flames (1-1).
Hugh Greenwood had nine points and nine rebounds for New Mexico, which shot just 27.8 percent (5 for 18) from the floor in the second half.
Hayden Humes led UIC with 16 points, Gary Talton added 14 and Barnes 11.
New Mexico will now face George Mason on Sunday at 6 p.m. UIC will face Mercer on Saturday at 2:30 p.m.