The Braves (7-11, 4-2 Southwestern Athletic Conference) shot 51 percent from the field. Twann Oakley had 16 points on 4-of-5 shooting from beyond the arc and dished out five assists.
UAPB (4-13, 2-3) was held to 17-of-44 shooting (38.6 percent) and committed 15 turnovers. Davon Haynes led the Lions with 22 points and 10 boards.
Alcorn State broke a 13-all tie as Luckett scored seven points to spark a 9-0 run, and the Braves coasted to a 33-20 halftime lead.
Haynes hit a layup in the second half to make it 40-27, but Alcorn State pulled away as Oakley hit two late 3-pointers to push the Braves' lead to 25.
Alcorn State has won four straight after dropping its first two conference matchups.