Martez Carter returned a kickoff 92 yards for a touchdown to give the Tigers (3-3, 3-0 Southwestern Athletic Conference) a 31-22 lead in the fourth quarter and Williams added a 6-yard touchdown pass to Verlon Hunter.
Williams finished 23-of-37 passing for 291 yards with an interception. He led the Tigers with 62 yards rushing. His other scoring pass went 13 yards to Chester Rogers for a 24-16 lead with 40 seconds remaining in the first half. Jestin Kelly ran 2 yards for the game's first score and Grambling never trailed.
Jaymason Lee threw a touchdown pass and two interceptions for the Bulldogs (2-4, 1-2) in their home opener. Harvey Harris ran for two scores and Brandon Eldemire one. Montaurius Smith had 131 yards receiving and a touchdown.