Williams completed 19 of 27 passes for 377 yards and added 52 yards rushing on eight carries.
Grambling State (5-3, 6-0 Southwestern Athletic Conference) took a 28-18 lead into halftime before scoring the first 21 points of the second half to put the game out of reach.
UAPB (1-5, 0-4) took a 3-0 lead when Tyler Strickland kicked a 31-yard field goal with 6:48 left in the first quarter. Sixteen seconds later, Williams connected with Verlon Hunter for a 73-yard touchdown and Grambling State never trailed again.
Hunter had 111 yards on two receptions, both for scores.
Benjamin Anderson passed for 467 yards and accounted for four touchdowns, but threw a pair of interceptions in the loss.