Chicago State tied the game on Jawad Adekoya's 3-pointer with 21 seconds to play.
Alabama State erased a six-point deficit with a 9-0 run, starting with a 3-pointer by Jamel Waters with 4:51 to go. Corvon Butler's two free throws made it 62-59 with 1:13 left. But Jordan Madrid-Andrews cut it to one with a layup and, after two more free throws Adekoya, hit the key 3 for the Cougars.
Elliott Cole and Madrid-Andrews had 13 each for the Cougars (3-4), who had 26 turnovers.