Jacksonville State (9-13, 2-6) trailed by 11 with 9:19 left, but used a 16-7 run, capped by Malcolm Drumwright's jumper - to cut it to two with 1:03 left.
Drumwright made a steal and layup to tie it at 62 with 39 seconds left, then Collins put Morehead back up with two free throws.
Drumwright then made 1 of 2 from the line, and fouled on the miss. Warner added a pair of free throws to seal the win.
Warner finished with 15 points for the Eagles.
Darion Rackley led Jacksonville State with 16 points. Drumwright ended with 10.