Hill was 17 of 31 for 278 yards and an interception and ran for 36 yards. Jamaal Williams ran for 79 yards on 14 carries for BYU (3-2) and Justin Sorenson kicked a 27-yard field goal.
Chuckie Keeton and Craig Harrison threw touchdown passes for Utah State (3-3). Keeton left with a knee injury with 4:06 left in the first quarter after a third-and-15 running play. He was on the sideline on crutches during the second half as the Aggies' nine-game home winning streak ended.
Leading 17-7 at halftime, BYU struck quickly in the third quarter. Hill hit Matthews with a 6-yard fade pass to the corner of the end zone early in the quarter, and Matthews then hauled in a 43-yard pass with 5:52 left in the quarter to make it 31-7.
Harrison was 5 of 5 passing with one TD on the season before taking over for Keeton. Harrison found Ronald Butler on an 8-yard pass for a late-game touchdown. The junior had 185 yards on 18-of-41 passing and ran for 38 yards. Joey DeMartino ran for 80 yards on 16 carries.
BYU scored on the first play from scrimmage when Van Noy grabbed Keeton's pass at the line of scrimmage and ran 15 yards untouched for a touchdown. Just moments later, Utah State stripped Hill of the ball, with Brian Suite recovering the fumble. Three plays later, Keeton found Travis Van Leeuwen with a 7-yard TD pass.
The Cougars took a 17-7 halftime lead after Hill found Matthews for a 30-yard touchdown pass with 10:40 to play in the second quarter.
Van Noy's score was only the third time in 22 games that Utah State had allowed a first-quarter touchdown, dating to the 2011 season. It was Keeton's second interception of this season.