McCoy completed 13-of-21 passes for 190 yards and the two TDs to lead the unranked Longhorns (4-2, 3-0 Big 12) to a high-profile win in the annual Red River Rivalry with the Sooners (5-1, 2-1) who lost to Texas for the first time since 2009.
There was much media speculation in Texas before the game that longtime Texas coach Mack Brown's job depended on a positive outcome Saturday.
McCoy completed a 59-yard TD play to Marcus Johnson with 8:46 to play in the second quarter and then connected with Mike Davis for a 38-yard score with 21 seconds to play in the third. Anthony Ferra kicked two field goals.
Johnathan Gray and Malcom Brown both rushed for more than 100 yards for the Longhorns, who racked up 225 yards on the ground and 445 yards overall.
Blake Bell was 12-of-26 for 190 yards for Oklahoma. He connected for two scores and Damien Williams ran for a TD.