Jacksonville State (3-5) built a 10-point lead at halftime, but Chicago State trimmed the lead throughout the second half. Durham's free throw with 20 seconds left put Jacksonville State up by three.
Kieran Woods and Trayvon Palmer both missed 3-pointers as time expired and the Gamecocks held on to break a four-game losing skid.
Durham was 6 of 9 from beyond the arc. Jared Hamilton had 17 points - a career high - and six rebounds, while Malcolm Drumwright added 14 points and six assists.
Chicago State (3-3) was led by Woods with 24 points. Elliott Cole finished with 17 points and was 4 of 9 beyond the arc.