"I don't know what to say," said BYU head coach Bronco Mendenhall. "That was this wildest game I've ever been a part of. That was amazing."
Hill led BYU 41 yards to the winning touchdown and Alani Fua iced the game, intercepting 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).
"Our coaches did a great job preparing us for this," said BYU QB Taysom Hill. "We knew it was going to be a shoot out. Luckily, we came out on top. It was a fun win."
O'Korn nearly matched Hill going 29 for 45 for 363 yards and three touchdowns. Both quarterbacks threw 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.
"It was an amazing game. It was an amazing game to be a part of," said BYU WR Skyler Ridley. "Resilient is how I would describe how we played. We kept coming back. To have the game winning drive is indescribable."
Houston (5-1) scored via the big play, including a 95-yard kickoff return by DeMarcus Ayers, while six of BYU's eight scoring drives went for 70 yards or longer.