Hill started at quarterback for BYU in place of the injured Riley Nelson, but he could not generate any points until the last minute of the half.
Neither team scored on its first possession; the Cougars drove to the Aggies 30-yard line but were stopped on fourth-and-1.
However, USU put together its second-longest drive of the season, 13 plays, on its next possession and drove to the BYU 1-yard line before settling for Josh Thompson's 26-yard field goal.
USU still has not allowed an opponent to score in the first quarter this season. BYU has not allowed an offensive touchdown in 11 quarters.
The Cougars drove to the Utah State 17 midway through the second quarter, but Justin Sorensen's 34-yard field goal attempt was blocked. It was the third time in four games that the Cougars have had a kick blocked.