Harrison passed for 221 yards in three quarters of play for the Aggies (5-3, 2-1 Mountain West Conference) before leaving with a leg injury on the final series of the third quarter. He was replaced by freshman Kent Meyers.
Hill ran for 48 yards and had 69 receiving yards. JoJo Natson caught a 71-yard Harrison pass for a score in the second quarter.
UNLV scored twice in the second quarter and the first half ended with a 17-13 USU edge.
The Aggies then scored 17 straight points in the second half including Harrison's 69-yard TD pass to Hill and a 49-yard field goal by Nick Diaz.
Blake Decker was 22-of-38 for 267 yards and three touchdowns for the Rebels (2-6, 1-3). He was sacked eight times.