Williams' layup with 17:29 to play gave Prairie View a 40-29 lead, but the Jaguars used a 15-6 run over the next seven-plus minutes, and cut the lead to 46-44 on Banks' 3-point play with 9:52 left.
But with 4:19 to go, Johnson buried a 3 to push the lead to 62-53 to seal the game.
Prairie View's bench outscored Southern's 35-9. With the loss, Southern fell to 0-2 in conference for the first time since the 2009-10 season.
The Panthers snapped a 14-game losing streak dating to last season.