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.
Officials: North Carolina must show proof of discrimination-free zone, or lose NCAA tournament games
North Carolina must prove to the NCAA that its host arenas will provide a discrimination-free zone, or risk losing NCAA tournament games in 2017 and 2018, multiple officials told ESPN.
Jalen Rose and David Jacoby examine the new NCAA draft rule and consider how it would have affected "The Fab Five."
Florida and Duke will meet on Dec. 6 in the Jimmy V Classic at Madison Square Garden as one of two high-profile games to help raise funds for cancer research.