SIU-Edwardsville (3-7) forced Chicago State, which shot just 16 of 53, into 25 turnovers, turning the miscues into 19 points.
After a couple of early ties, Nunn hit a 3-pointer as Edwardsville broke away on a 13-2 run and never looked back. The Cougars made 18 of 47 shots - hitting 8 of 17 3-point attempts. Nunn added three steals and eight rebounds.
The 38 points was the fewest allowed by SIU-Edwardsville against a Division I opponent.
Rahjan Muhammad led Chicago State (3-11) with seven points. Clarke Rosenberg, who became the ninth Chicago State player to break past 1,000 career points last week, was blanked on 0-of-6 shooting. Rosenberg has 1,032 points, eighth on the all-time list.