Prudhomme's 3 gave the Jaguars a 71-69 lead. Trelun Banks then stole the ball from Zay Jackson, got fouled and hit two free throws with three seconds to play to seal the win for Southern (5-1) which has won five straight.
Southern led 65-57 with 4:20 to play before Southeastern Louisiana (2-7) went on a 12-3 run and took a 69-68 lead on two free throws by Jackson with 27 seconds left.
Adrian Rogers finished with 18 points and Banks added 13 for the Jaguars.
Southern led 35-33 at the half and used a 10-1 run after the break to take a 45-34 lead on a 3 by Banks.