Bergeron ran for 110 yards and two scores while Brown added 105 yards and one touchdown for the 15th-ranked Longhorns (1-0), who trailed 9-7 after the first quarter.

Texas surrendered 178 yards in the first period, nearly half of it coming on Brett Smith's 82-yard touchdown pass to Robert Herron.

Texas took the lead for good at 14-9 on David Ash's 16-yard TD pass to Jaxon Shipley midway through the second period. The Longhorns led 24-9 at the half.

Ash, who won the starting job in the final week of preseason practice, completed 20 of 27 passes for 156 yards.

Wyoming (0-1) closed within 31-17 early in the fourth on Smith's second TD pass to Herron, this one a 22-yarder, but Texas clinched the win on Bergeron's 17-yard scoring scamper with 8:48 left.

Smith finished 16 of 28 for 276 yards.

GAME NOTEBOOK: Texas improved to 100-17-3 in openers and 78-7-2 when opening at home. Mack Brown is 14-1 in openers at Texas. ... Brown won his 228th career, four behind Hayden Fry for 12th on the all-time list. ... Texas held Wyoming to 69 yards rushing.