The Hornets (11-16, 8-6 Southwestern Athletic Conference) led 31-21 at halftime, holding the Braves (3-21, 3-11) to their lowest first-half total of the season.
A flagrant foul early in the second half by Alcorn State gave Alabama State's Tramaine Butler a free throw, and Kenderek Washington followed with a 3-pointer to push the Hornets' lead to 38-21.
The Hornets later went up by as many as 20 after back-to-back 3s by Moorer for a 42-32 lead. Alabama State improved to 7-1 when Moorer is in the lineup.
Washington added 12 points and Chris Duncan had a near triple-double with nine points, nine rebounds and seven blocks for the Hornets, who won their fifth straight.
Marquis Baker scored 12 points for the Braves.