Rodgers made 8 of 16 field goals and 7 of 8 free throws and Banks made 14 of 17 free throws.
A jumper by LSU-Alexandria's Andre Gonzaque with 8:02 left in the first half made it 17-16, but Southern (1-1) responded with a 12-0 run, including six points by Rodgers, pushing its lead to 13.
LSU-Alexandria closed the first half with a 5-0 run to make it 32-25, but would get no closer.
Southern scored 34 points in the paint and attempted just three 3-pointers. The Jaguars made 34 of 41 free throws.
The game served as an exhibition for LSU-Alexandria, which was led by Darius Johnson's 20 points. DeAngelo Coleman scored 12 and Darryl Millburn added 11.