Keenum completed 30 of 40 passes without an interception in his first game since tearing his right anterior cruciate ligament early in a loss to UCLA last September in the Rose Bowl. The NCAA granted him a sixth year of eligibility in January, allowing Keenum to resume his pursuit of several NCAA records.
He looked like his old self, and so did the Cougars' powerful offense, gaining 469 total yards.
The Bruins finished with 554 yards, but their defense couldn't stop Keenum and the Cougars.
Keenum was sharp from the start, completing 5 of 7 passes on Houston's opening drive. He also scrambled out of trouble twice, picking up a first down on a 10-yard scamper to the UCLA 7. Michael Hayes, one of three running backs who carried on the Cougars' first series, scored on a 1-yard run with 9:06 left in the first quarter.
The Bruins went three-and-out, and Keenum went back to work, completing four straight passes for double-digit gains. The drive stalled at the UCLA 18, and the Cougars settled for Matt Hogan's 35-yard field goal.
UCLA gained only 29 yards in the first quarter, but Prince started the second with a 29-yard pass to Joseph Fauria to the Houston 18. Johnathan Franklin weaved for a touchdown on the next snap to cut the deficit to 10-7. Franklin rushed for 128 yards on 16 carries in the game.
Bruins' defensive tackle Cassius Marsh sacked Keenum on Houston's next play, leading to the Cougars' first punt. The crowd fell silent for a moment, but Keenum sprang back up.
Prince was then knocked out of the game with a concussion when Houston cornerback D.J. Hayden upended him on a scramble along the sideline. Brehaut, who started seven games in 2010, came in as trainers attended to Prince.
The Cougars led 24-14 when they got the ball back on their own 36 with 35 seconds left in the half. That was plenty of time for Keenum, who threw a 26-yard pass to Carrier, got help from a UCLA pass-interference penalty, then found Carrier again for a 23-yard touchdown with eight seconds to spare before the break.
Keenum was 19 for 24 for 188 yards in the first half.
Brehaut's first pass of the second half was a 54-yarder down the middle to Nelson Rosario. Derrick Coleman's 1-yard touchdown run cut it to 31-21 with 8:28 left in the third quarter.
The Cougars were threatening again, but Beall fumbled inside the 10. A 29-yard run by Franklin gave UCLA some breathing room, and Brehaut scored in the final minute of the third quarter to pull UCLA within three.
Houston nearly gave away another costly turnover early in the fourth quarter, when Carrier took a short pass and fumbled at the 1. But Houston center Chris Thompson fell on the bouncing ball in the end zone, and after an officials' review, the play was ruled another Cougars' touchdown.
The Bruins chewed up seven minutes on their ensuing drive, and Kip Smith missed a 32-yard field goal try with 2:29 left.
UCLA has lost three of its last six road openers, including its last two. Houston improved to 27-5 at home since the start of the 2006 season.