Case McCoy threw for 168 yards and two of-15 passing and the Texas defense forced four turnovers, as 20, at the Rose Bowl.
Malcolm Brown ran 22 times for 110 yards and a score, while Foswhitt Whittaker ran for 63 yards and two touchdowns for the Longhorns (3-0).
D.J. Grant caught six passes for 77 yards and three scores, while Mike Davis hauled in three passes for 77 yards.
Kevin Prince had a rough day in defeat, throwing for only 26 yards and three interceptions before getting pulled in the first quarter in favor of Richard Brehaut.
Brehaut completed eight of his 19 passes for 150 yards, while John Franklin ran 15 times for 58 yards and Derric Coleman ran for 47 yards and two touchdowns.
Nelson Rosario grabbed four passes for 68 yards as UCLA (1-2) couldn't sustain momentum from its win over San Jose State last Saturday.
Early in the first quarter, Texas struck first. Following a Prince interception, the Longhorns began the ensuing drive in UCLA territory. On the third play of the drive, McCoy found Grant wide open over the middle for a 45- yard score to put Texas up 7-0.
"He did a good job on numerous plays. I thought he played well for his first start," Texas head coach Mack Brown said. "He's played better in games than he has in practices. I didn't know how much time each quarterback would earn, but Case had a great day today."
Late in the opening quarter, Texas added to its lead when the Longhorn defense picked off Prince for a second time and began the next drive on its own 29. The offense marched 71 yards and capped the drive with an eight-yard touchdown run by Whittaker for a 14-0 lead.
Following the touchdown, Prince was intercepted for a third time on the ensuing UCLA drive and Texas took over with great field position, starting at its own 43-yard line. The Longhorns swiftly moved the ball down the field, going 57 yards in seven plays and the drive was capped by a 16-yard touchdown run by Brown to put Texas up by three scores.
UCLA got a much-needed touchdown midway through the second quarter to get back into the game. After Prince threw three picks, UCLA coach Rick Neuheisel went with Brehaut to try and turn the momentum. The move paid dividends immediately.
With Brehaut under center, the Bruins offense clicked on all cylinders and they marched 74 yards in 11 plays before Coleman punched the ball into the end zone from the one-yard line.
"I thought Richard played well," Neuheisel said. "I'm anxious to look at the tape. He settled the offense down. He has surged to the lead, no question."
Texas poured in another score with only seconds remaining in the first half to take a 21-point lead. Texas went 59 yards in 11 plays to record the score, but the key play of the drive came with Texas facing 3rd and 18 from the UCLA 27- yard line. McCoy showed his athleticism as he scrambled to his right out of the pocket and found Davis wide open along the sideline for a 25-yard gain and a first down. From the Bruins two, McCoy found Grant in the end zone.
The Bruins pulled some momentum back right before the break as Jeff Locke blasted a 51-yard field goal through the uprights to make it 28-10.
Locke connected on another long field goal attempt on UCLA's first possession of the second half, this one from 49 yards out to make it 28-13.
But McCoy and the Texas offense kept buzzing. On the ensuing possession, the Longhorns marched 71 yards in six plays, highlighted by a big 45-yard completion to Davis on third down, and Grant caught a five-yard touchdown pass to make it a 35-13 game.
UCLA scored on its next possession as Brehaut led the Bruins on a 10-play, 55- yard drive. Franklin ran right up of the gut of the Texas defense down to the five-yard line and Coleman finally was able to push his way into the end zone on fourth-and-goal after being stopped on his first three tries.
Texas again had an answer, as Whittaker burst through the line unblocked for a 36-yard touchdown run and a 42-20 lead.
The Longhorns put the icing on the cake with about three minutes to go in the game when Cody Johnson finished off an 11-play, 50-yard drive with a seven- yard touchdown run to account for the final score.
It was McCoy's first career collegiate start. His older brother Colt, who now is the starting quarterback for the Cleveland Browns, also played for Texas... This marks the fifth straight year and ninth time in the 14 years under head coach Mack Brown that the Longhorns have opened the season with at least three straight wins.