Hanson had earlier made good on a 38-yard attempt that gave the Hornets (2-3, 1-1 Southwestern Athletic Conference) a brief 25-22 edge.
Alcorn State's Corey McCullough finally hit a field goal - from 39 yards - to tie the game and send it into the fifth overtime. He missed six attempts on the day, including one from 29 yards that would have won it for the Braves as regulation time expired.
KHA'Darris Davis threw for 155 yards and two touchdowns for the Hornets.
Davis threw a pair of touchdowns in the first quarter, one to Joe Williams and the other to Michael Jefferson, and the Braves led 14-7 at halftime.
De'Shawn Waller ran for 214 yards and two touchdowns for the Braves (4-2, 3-1), including one early in the fourth quarter that tied the game 14-all, setting up the first overtime period.
Copyright 2018 by AP. Any commercial use or distribution without the express written consent of AP is strictly prohibited.