DALLAS—Mack Brown can finally say he’s done something in the Texas-Oklahoma game that Bob Stoops hasn’t—pulled off an upset. And it’s a big one.

Brown’s Longhorns grabbed some second-half momentum by foiling a fake punt Saturday, then Colt McCoy and the defense built on it, carrying No. 5 Texas to a 45-35 victory over No. 1 Oklahoma.

The Longhorns outscored the Sooners 25-7 after stopping the trickery, and their half of the record crowd of 92,182 fans loved every bit of it. When Oklahoma’s game-ending heave was picked off in the back of the end zone, Texas defensive end...

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