The victory gave the Tigers (7-4, 6-3) the West Division title in the Southwestern Athletic Conference. Grambling State will play against SWAC East Division winner Alabama A&M (8-3, 7-2) in the championship game Dec. 10 in Birmingham, Ala.
Grambling State, which is riding a six-game winning streak, has won four straight Bayou Classics.
The Jaguars (4-7, 4-5) were 2-2 in their last four games of the season.
Williams, a freshman, completed 11 of 17 passes for 174 yards with one interception.
The Tigers led 10-0 with 9:44 left in the second quarter when Williams lofted a 27-yard touchdown pass to Louis, who outjumped Southern's Virgil Williams in the end zone.
Williams also threw scoring passes of 34 and 12 yards to Louis.