Jones went 36-of-51 passing for the Sooners (4-0), who nearly saw a 15-point lead evaporate due to a pair of critical errors late in the game before clamping down for the win.
Ryan Broyles extended his streak of consecutive 100-yard games to six with 10 catches for exactly 100 yards. DeMarco Murray contributed 67 yards and a score on 28 carries for Oklahoma.
The Bearcats (1-3) fell to 0-2 all-time against Oklahoma. They were led by Zach Collaros, who went 23-of-38 passing for 305 yards and three touchdowns, allowing one interception.
Wideout D.J. Woods hauled down seven passes for 171 yards and a score, but his muffed punt led to the Sooners' final touchdown.