Baylor (1-1) scored on its first five possessions and won for the first time since it beat Buffalo last Sept. 22.
Griffin, a true freshman, completed his last nine passes and was 15-of-19 for 294 yards in a little more than 2½ quarters to help Briles, who coached Houston the past five seasons, pick up his first Baylor victory.
Jay Finley rushed for 91 yards and scored three touchdowns for the Bears, who jumped out to a 23-0 first-quarter lead against the Demons.
Northwestern State (1-1) didn’t get a first down until early in the second quarter. By that time, Baylor was up 30-0.
Baylor, which had 537 yards total offense, sputtered early offensively in a 41-13 home loss to No. 20 Wake Forest last week before the athletic Griffin came off the bench to provide somewhat of a spark.
The Bears had no such problems against Northwestern State as Griffin threw his first career touchdown pass came on Baylor’s first possession.
He hit Ernest Smith, who caught the ball over defender Cashas Pollard near the goal line, on a 49-yard scoring connection on third-and-16 that gave the Bears a 6-0 lead.
Baylor linebacker Antonio Johnson recovered Byron Lawrence’s fumble to set up the Bears’ second touchdown, Finley’s 40-yard TD run.
After Ben Parks kicked a 20-yard field goal to put Baylor ahead 16-0, Chris Francis intercepted John Hundley’s pass to give the Bears the ball at the Demon 19.
Hundley, who was pulled for one possession after the interception, was 16-of-28 for 127 yards.
Griffin scored on a 3-yard run three plays later to give the Bears a 23-0 cushion. It was the most points for Baylor in a first quarter since it scored 24 against Rice on Nov. 14, 1992.
Finley scored on a 35-yard run early in the second quarter to cap the early flurry.
Northwestern State managed a pair of Robert Weeks field goals before halftime to cut Baylor’s advantage to 30-6.
The Bears had 308 yards total offense by halftime - more than they had the entire game against Wake Forest.
Griffin added a 32-yard touchdown pass to Thomas White and a 47-yarder to Finley to cap his evening.
Baylor improved to 14-0 against I-AA teams, while the Demons dropped their seventh straight against Football Bowl Subdivision teams since they beat Louisiana-Monroe in 2005.
