Jackson hit 6 of 9 from 3-point range for the Golden Lions (9-13, 8-2 Southwestern Athletic Conference), who have won five of their past six and eight of 10 since snapping a nine-game losing streak.
Hammond's free throw with 31 seconds left put Arkansas-Pine Bluff up 78-74. Joshua Freelove hit a 3 for Alabama State with 25 seconds left, but Hammond hit a free throw and then a layup as the Hornets' last two possessions ended in a turnover and a missed 3-pointer.
Freelove led Alabama State (6-17, 4-6) with 29 points on 11-of-17 shooting, making 6 of 9 3-point attempts. Phillip Crawford added 21 points and nine rebounds.
Colorado State graduate transfer John Gillon has chosen Syracuse, giving the Orange a potential starter at point guard entering the 2016-17 season.
DeSean Murray, who averaged 20.2 points as a sophomore at Presbyterian, will transfer to Auburn to play for coach Bruce Pearl.
Former Kentucky guard Ed Davender, the only Wildcat with at least 1,500 points and 400 assists, has died. He was 49.