The Coogs ended the first half of the game 21-10 and fought hard to make a comeback during the second half, but fell 49-31.
UH finished last season 8-5 and lost to Army in the Armed Forces Bowl.
Oklahoma won its fourth consecutive Big 12 Championship last season, and finished with a record of 12-2.
The Sooners lost to Georgia in the opening round of the College Football Playoff.
Oklahoma got on the board first Sunday, with a quick opening drive after halting the Cougars' offense.
Jalen Hurts found Jeremiah Hall for the 14-yard TD, capping off a 3-play, 61-yard drive.
The Cougars were only able to rack up 21 yards in the opening quarter, and all of them were rushing yards. They were only able to get one 1st down compared to 13 for Oklahoma.
Oklahoma took a 14-0 lead in the opening minute of the 4th quarter with a rush TD from Hurts, who got some help from his offensive line as they pushed him into the end zone.
A 45-yard TD connection between Hurts and CeeDee Lamb gave the Sooners a 21-0 lead over the Cougars midway through the second quarter.
UH finally got on the board when Deriq King and Kyle Porter connected on a 23-yard TD. It capped off a six-play, 81-yard drive.
That TD drive was the first time in the first half the Cougars were able to get any offensive rhythm.
RELATED: Holgorsen making UH debut vs. team he has yet to beat in 7 tries: OU
He, along with Oklahoma head coach, Lincoln Riley, are two of the brightest offensive minds in college football.
The other big story: the quarterbacks.
Oklahoma quarterback Jalen Hurts played the last three seasons at Alabama. He played high school football at Channelview and even played against UH quarterback, D'Eriq King when he was at Manvel.
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SEE MORE: University of Houston football preparing for new era under Dana Holgorsen