Alcorn State took a 37-35 lead early in the second half but did not score again for four minutes and trailed 44-39. Southern extended its lead to 51-41 on Rodgers' 3-pointer midway thought the half and Jaguars cruised from there.
Reginald Johnson scored 14 points for Alcorn State (8-12, 6-3), which had won five straight for the first time since 2005. Octavius Brown had 13 points, Tamarcio Wilson added 12 and Patrick Onwenu 10.
Alcorn State pulled to 24-22 with 1:53 left in the first half but Southern closed on a 4-0 run for a 28-22 halftime lead.