Hill led BYU 41 yards for the winning touchdown and Alani Fua iced the game, intercepting freshman John O'Korn to end Houston's hopes.
Known for his running ability, Hill went 29 for 44 for 417 yards and four touchdowns to lead BYU (5-2).
O'Korn nearly matched Hill going 29 for 45 for 363 yards and three touchdowns. Both had three interceptions, but O'Korn's final pick proved the most costly as it came on the game's deciding play.
The teams combined for 1,164 yards with only one drive longer than three minutes. Houston (5-1) scored via the big play while six of BYU's eight scoring drives went for 70 yards or longer.
The offensive explosion of the first half made way for a defensive battle as the teams combined for just nine points in the second half.
Derrick Mathews notched back-to-back sacks, including a safety for the only points of the third quarter to give Houston a 40-34 lead. It was the first safety by Houston since 1993.
Hill rekindled his first half rhythm hitting Cody Hoffman for a 25-yard touchdown pass to give BYU a 41-40 lead. Hoffman's touchdown was the 30th of his career, tying him for the school record.
Houston looked poised to respond immediately as O'Korn hit a 76-yard pass to Spencer to set up 1st-and-goal from the 4. After two failed attempts and a sack, Houston missed a 40-yard field goal.
In the end, Hill and BYU struck last to claim the road win
BYU got off to a quick start when Spencer Hadley intercepted O'Korn on the first play of the game. Three plays later Jamaal Williams ran in a 15-yard touchdown to give BYU a 7-0 lead.
The hometown Cougars followed BYU's first 10 points with a 95-yard kickoff return for a touchdown from DeMarcus Ayers. Change of pace quarterback Greg Ward, also a freshman, then hit Xavier Maxwell for a 69-yard touchdown.
On the ensuing drive Houston got a second non-offensive touchdown when Mathews, who added three sacks, scored on a 29-yard interception return for a brief first quarter 21-17 lead.
Hill threw two first quarter touchdowns to Ross Apo, 11 and 18 yards, as BYU re-claimed a first quarter lead 24-21.
Houston's defense started to respond in the second quarter. They stopped four of BYU's six drives in the second quarter and held the visitors to 10 points.
O'Korn and the offense heated up as well. The freshman hit touchdown passes of six yards to Deontay Greenberry and connected with Daniel Spencer to spark a dazzling 41-yard catch-and-run to help Houston to a 38-34 first half lead.
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