AUSTIN, Texas (AP) -- After winning the starting job in training camp, Texas quarterback David Ash said he'd be happy to hand off and get out of the way if it meant the Longhorns would win.
While Ash was efficient and mostly mistake free in moving Texas on long scoring drives, Bergeron and Brown battered Wyoming and delivered the knockout blow late in the fourth quarter to put the game away.
Bergeron ripped a 53-yard run up the middle from the Texas nine, then capped the drive with a 17-yard touchdown, his second of the night, with 8:48 to play.
Bergeron finished with 110 yards and two touchdowns and Brown ran for 105 yards and a third-quarter touchdown for Texas.
''The more the game wears on, those guys can make some plays by breaking tackles,'' Texas coach Mack Brown said. ''You want to just keep bringing it.''
Robert Herron had touchdown catches of 82 and 22 yards for Wyoming (0-1). Cowboys quarterback Brett Smith passed for 276 yards but threw two interceptions in the second quarter that set up Texas touchdowns.
''I can't make those stupid mistakes because against a team like that, they're going to capitalize on it,'' Smith said. ''I can't put the defense in holes like that.''
Ash, who won the starting job over Case McCoy after those two shared starts in 2011, was an efficient 20-of-27 passing for 156 yards and a touchdown to Jaxon Shipley.
Ash was dogged by interceptions last season and spent most of the game throwing short passes to the sideline and to his running backs to keep drives alive. His only big mistake was a fumbled snap after Herron's second touchdown had pulled Wyoming within 31-17.
''It's my job to just go out there and operate and manage the game,'' Ash said. ''I was trying to move the chains... get it in somebody's hands and let them make a play.''
Texas needed the big plays from its defense. The Longhorns were scoreless on three of their first four possessions before the two interceptions flipped momentum.
Kenny Vaccaro's interception led to Ash's 16-yard touchdown pass to Shipley. Vaccaro then pressured Smith into making a bad throw that was picked off by Carrington Byndum to set up D.J. Monroe's 7-yard touchdown run.
Texas was seemingly on its way to an easy win until Herron made an acrobatic grab for his second touchdown and Wyoming got the ball back after Ash's fumble.
The Cowboys converted one fourth down but was stopped on another when Smith was tackled a yard short of the marker. Bergeron then burst up the middle for his big run. His second touchdown came when he broke through the line to his left and rumbled to the end zone.
''We thought we were going to score another touchdown and make it a one-score game,'' Wyoming coach Dave Christensen said. ''That's why we went for it on fourth down. A field goal wouldn't have helped us.''