The junior quarterback completed 28 of 36 passes to nine receivers without an interception. He went 17 of 20 to lead the Cougars to a 28-7 halftime advantage, and was BYU's leading rusher with 97 yards on 12 carries.
The Huskies gave up 513 yards of offense, but were able to hold BYU in check for much of the second half.
UConn's Casey Cochran and Chandler Whitmer split quarterback duties and threw for a combined 284 yards. Cochran was 17 of 31 for 171 yards. He also threw an interception on the Huskies' second drive deep in BYU territory. Whitmer was 8 of 17 for 113 yards.
BYU played without a handful of regulars. Tailback Jamaal Williams and wide receiver Devon Blackmon announced their own suspensions for school honor code violations. Defensive tackle Marques Johnson and starting cornerbacks Jordan Johnson and Robertson Daniel also were suspended for unspecified violations of team rules. Receiver Nick Kurtz missed the game because of a stress fracture in his foot.
UConn turned the ball over on its first two possessions, helping BYU take a 14-0 lead.
Hill capped the Cougars' opening 15-play, 75-yard drive with a 7-yard run. He then found Mitch Mathews wide open over the middle from 26 yards out, after tailback Max DeLorenzo fumbled on the Huskies' first offensive play.
Hill added a 26-yard touchdown run to complete a 90-yard, fourth-quarter drive that sent the fans to the exits.
Penalties slowed the Cougars a bit. They committed 15 of them for 150 yards. UConn was flagged eight times for 90 yards.
A fumble by BYU's Mathews at midfield led to UConn's only touchdown. Whitmer led the Huskies on a six-play drive that ended with freshman Josh Merriner scoring from a yard out in the second quarter.
Bobby Puyol made a 35-yard field goal for UConn in the fourth quarter.
Hill danced away from pressure late in the first half and found Terenn Houk open to his left for a 35-yard touchdown catch-and-run that made it 28-7 at the half.
The Huskies put together an 11-play drive to start the second half, but failed after faking a 40-yard field goal.
UConn's top receiver, Geremy Davis, finished with seven catches for 96 yards. He spent some time in the fourth quarter in the locker room, but returned before the end of the game.
BYU next plays at Texas September 6th.