Bernard had a triple-double with 14 points, 12 assists, 11 rebounds and four steals. Justin Ravenal made four 3-pointers and scored 16 points off the bench in 18 minutes of play.
Florida A&M (3-4) led 38-32 at halftime but Alcorn State took a 10-point lead in the second half.
The Rattlers made eight 3-pointers on 16 attempts while the Braves were 3 for 19 from distance.
Devonte Hampton, DeAndre Davis and Reginald Johnson each scored 14 for Alcorn State (0-5). Davis was 7 for 8 from the field. Marquis Vance and Patrick Onwenu had 10 points apiece, and Vance also grabbed 10 rebounds.