Hill completed 27 of 41 passes to lead the Cougars (6-2) to their fifth straight victory and their first in the four-game series with Boise State (5-3). Jamaal Williams ran for 107 yards.
Grant Hedrick threw for 232 yards and a touchdown in his first start for the Broncos and Jay Ajayi ran for 151 yards. Boise State was unable to overcome four turnovers three straight in the second half and failed to give Chris Petersen a victory in his 100th game as head coach.
BYU ended Boise State's 50-game October winning streak that dated to a 45-14 loss to Rice in 2001.
Hill dominated from start to finish. In the first half, the sophomore threw for 253 yards and two touchdowns, ran for a score and had 306 yards of offense.
Boise State had trouble figuring out BYU's defense early. The Broncos had only 37 yards of total offense and one first down in the first quarter.
The Cougars had 203 yards in the first quarter. They attacked the Broncos with a mix of runs and short passes. It paid off when Hill broke free for a 20-yard scamper into the end zone to open the scoring.
The Cougars made it 10-0 on Justin Sorensen's 28-yard field goal to open the second quarter. Boise State answered with Dan Goodale's 33-yard field goal.
BYU broke it open before halftime with big plays on both sides of the ball. BYU needed only 59 seconds to answer Boise State's field goal, going up 17-3 on Hill's 37-yard pass to Ross Apo. Three minutes later, the Cougars made it 24-3 on Cody Hoffman's 4-yard reception the school-record 31st TD catch of his career.
BYU set up Hoffman's touchdown with a fumble recovery. Craig Bills stripped the ball from receiver Shane Williams-Rhodes, and Remington Peck recovered at the Broncos 47.
In the third quarter, Ajayi had a 61-yard run to set up Goodale's 41-yard field goal.
The Cougars made it 31-6 when Hill hit Mitch Matthews for a 40-yard completion on a crossing route. Boise State finally got its first touchdown a short time later when Hedrick ran for 9 yards on fourth down and punched it in from 5 yards out to make it 31-13. Williams-Rhodes set up the score with a punt return to the BYU 22.
BYU forced turnovers on three straight Boise State drives. Kyle Van Noy recovered Geraldo Boldewijn's fumble, Skye PoVey picked off a pass from Hedrick on the next drive, and Remington Peck capped the turnover spurt by recovering Ajayi's fumble.
The Broncos managed to score another touchdown, making it 34-20 when Hedrick found Troy Ware with a 14-yarder with 10:23 left.
Sorensen also made field goals of 34 and 41 yards for BYU.