The Hornets (10-16, 7-6 Southwestern Athletic Conference) led 35-29 with 16:33 left to play before going on a 24-11 run over the next 9 minutes to stretch their lead to 59-40 -- their largest of the game.
Alabama State outrebounded the Jaguars 40-25 and posted a 26-22 scoring edge in the paint.
Quinton Doggett scored 10 points and grabbed eight rebounds to lead Southern, which has lost seven straight and eight of its last nine contests.
The Jaguars (4-22, 3-11) trailed 34-28 at halftime, but were unable to get back into the game after shooting 28 percent from the floor (7 of 25) in the second half.
The Hornets, who have won four consecutive games, had seven players score at least five points.