Murray's 20-yard TD run early in the fourth quarter put the Sooners up 28-10, but Texas mounted a comeback, scoring 10 late points to make a game of it. Aaron Williams, however, fumbled an Oklahoma punt with 1:02 remaining to ice the game for the Sooners (5-0, 1-0 Big 12).
Landry Jones connected on TD passes to Kenny Stills and James Hanna, racking up 236 yards through the air on 24-of-39 attempts as Oklahoma beat Texas for only the second time in six years.
The Longhorns (3-2, 1-1) saw their 13-game Big 12 winning streak snapped.
D.J. Monroe led Texas with a 60-yard touchdown run. Garrett Gilbert tossed for 266 yards with an interception on 27-of-41 passing.