The No. 11 Longhorns, who led 28-27 coming out of the half, took the opening drive of the third quarter 54 yards on 13 plays. Anthony Fera's 38-yard field goal capped the drive, giving the Longhorns a 31-27 lead midway through the quarter.
No. 8 West Virginia would respond, however, with quarterback Geno Smith quickly leading the offense down the field and hitting Stedman Bailey for 9 yards and giving the Mountaineers a 34-31 lead.
Smith is 20-of-29 for 235 yards and three touchdowns so far in the game.
The Longhorns would use a balanced rushing attack between Joe Bergeron and Johnathan Gray on the next drive, going 58 yards on nine plays. Bergeron finished the drive with a 4-yard run to give Texas a 38-34 lead heading into the final 15 minutes.