The LSU defense was so dominant that the Cougars gained just 77 yards in total offense. By the time LSU took a 27-0 lead on Darrel Williams' 1-yard run with 8:12 left, the Cougars had picked up just five first downs to 24 for LSU.
The game was moved to New Orleans from Houston because of the devastating flooding in southeast Texas from Hurricane Harvey.
Guice scored from 4 yards and added a 1-yard burst to give LSU a 14-0 halftime lead. Williams gave Guice a breather in the second half and finished with 92 yards on 15 carries.
Quarterback Danny Etling had a clean game, completing 14 of 17 passes for 173 yards. Kicker Jack Gonsoulin added field goals of 23 and 20 yards.
The only two negatives in LSU's opening performance were a flurry of a penalties -- 10 for 86 yards -- and three red zone drives ending with two short field goals and a fourth-down tackle for loss.
But LSU finished the game with a 479-97 advantage in total offense and 25-6 edge in first downs. BYU dropped to 1-1 on the season.
The LSU defense suffocated BYU in the first half, holding the Cougars to just 47 yards in total offense.
Guice carried the ball 20 times in the first half for 90 yards, enough to move him past Heisman Trophy winner Billy Cannon into 16th place on LSU's all-time career rushing list.
Even though Guice was the focal point of LSU's offense, he did not look overburdened as LSU kept the BYU defense on its heels with the constant pre-snap motion and shifts designed by new offensive coordinator Matt Canada.
Etling was efficient, picking up a pair of third-and-8s on LSU's first touchdown drive with sideline passes to Derrick Dillon, and his 52-yard bomb to D. J. Chark to the BYU 2 in the second quarter set up Guice's second score.
LSU held a 269-47 edge in total offensive yardage and a 21:48 to 8:12 edge in time of possession in the first half