Tyrone Hanson added 19 points and six assists as the Tigers (16-14, 12-6 Southwestern Athletic Conference) ended a two-game losing streak and secured the second seed for the conference tournament, which begins Wednesday in Garland, Texas.
Jackson State trailed 57-56 with 5:51 left before going on a 15-4 run for a 71-61 lead with 38 seconds to play.
Jenirro Bush hit a jumper to give the Tigers the lead for good with 5:21 remaining and Maxey scored eight points, including a layup to cap the run and give Jackson State a 10-point lead.
There were 22 lead changes in the game.
De'Suan Dixon added 12 points and eight rebounds for the Tigers, who swept the Bulldogs.
Cornelius Hester scored 25 points and Jeremy Crutcher added 10 points for Alabama A&M (13-14, 10-8).