Keenum threw touchdowns to four different receivers and ran for another score as the Cougars (1-0) won the first meeting between the teams and improved to 32-30-2 in home openers.
Freshman Charles Sims caught six passes for a game-high 128 yards and scored his first career touchdown in the first quarter. Bryce Beall carried the ball nine times for a team-high 58 yards as the Cougars spoiled Bradley Dale Peveto's first game at the helm of the Demons.
The Cougars scored touchdowns on their first four possessions and led 28-0 with 2:30 left in the first quarter.
Less than four minutes into the game, Keenum completed a 23-yard touchdown pass to Sims. Beall followed that with a 17-yard TD run to make it 14-0 with 8:39 left in the first quarter.
When Houston got the ball back, Keenum and L.J. Castile hooked up on a 22-yard scoring pass. Sims then made it 28-0 in the first quarter with a 1-yard touchdown run.
Keenum, who completed his first nine passes, led the Cougars on a 98-yard drive to start the second half. He capped that drive with a 15-yard pass to Beall.
John Hundley completed 22 of 35 passes for 106 yards and a touchdown for Northwestern State. He finally got the Demons on the board with a 1-yard touchdown pass to Justin Aldredge with 2:49 left in the second quarter.
But after holding Houston to three-and-out on the next drive, the Demons turned the ball over on the ensuing punt, and Keenum scored his fourth touchdown of the night with a seven yard run to make it 41-7 at the half.
William Griffin finished with 10 carries and a team-high 63 yards on the ground for Northwestern State.