Jackson State's Pierre Crawford tied the game at 34 on a layup with 11 minutes remaining, but Rodgers scored five-straight during a 10-2 run that gave Southern (6-12, 3-1 Southwestern Athletic Conference) a 44-36 advantage with 7:31 left.
Javeres Brent made a 3 to pull Jackson State (4-13, 2-2) within four, 47-43, with four minutes remaining. Banks then converted a three-point play and the Tigers went 1 of 5 from the field over the next three-plus minutes as Southern extended its lead 58-47 with 28 seconds to play.
Raeford Worsham had 15 points and eight rebounds for Jackson State, which shot 34. 6 percent from the field and made just 11 of 20 free throws. Southern was 20 of 30 from the stripe.