Hill passed for 339 yards and three touchdowns and ran for 69 yards and another score and Jamaal Williams added 107 yards on the ground as the Cougars (6-2) posted 568 total yards and won their fifth straight game. In four October contests, BYU scored 31, 38, 47 and 37 points.
BYU's defense was vulnerable in the second half and allowed 493 yards in the game, but created four takeaways.
BYU dominated the first half with 376 total yards to Boise State's 203, while taking a 24-3 lead.
The Cougars gained 203 total yards on their first three possessions, but turned that production into only 10 points. Boise State's defense forced two field-goal attempts, with Justin Sorensen missing a 35-yard attempt and making a 28-yarder. In between, Hill ran 20 yards for a touchdown.
Boise State turned the ball over on downs at the BYU 12-yard line early in the second quarter, before launching another drive that resulted in Dan Goodale's 33-yard field goal to make it 10-3.
BYU answered quickly with a touchdown drive, topped by Hill's 37-yard pass to Ross Apo. The Cougars got the ball back via Remington Peck's fumble recovery and scored again on Hill's 4-yard pass to Cody Hoffman to make it 24-3.
After another Boise State field goal, the Cougars extended the lead to 31-6 on Hill's 40-yard touchdown pass to Mitch Mathews.
The Broncos later came within 34-20 on Grant Hedrick's 18-yard TD pass to Trevor Harman early in the fourth quarter. BYU answered with Sorensen's 41-yard field goal and then the Cougars made their second fourth-down stop of the game, taking over at their 44-yard line with 4:43 remaining.