Bell went 15-of-25 through the air 131 yards and an interception for the Sooners (6-1, 3-1 Big 12), who shook off last week's loss to Texas.
Damien Williams picked up 56 rushing yards on 15 carries and Sterling Shepard made seven catches for 82 yards and two touchdowns for Oklahoma, which improved to 21-0 since 2004 in games following a regular-season loss.
The Jayhawks (2-4, 0-3) dropped a third straight. Jake Heaps was held to just 5-of-13 passing for 16 yards and a touchdown.
James Sims led all rushers with 129 yards and two TDs on 23 carries.