Klein picked up 50 rushing yards on 15 carries while also racking up 145 yards through the air with an interception on 12-for-21 efficiency for the Wildcats (10-0, 7-0 Big 12).
The victory, coupled with current No. 1 Alabama's loss to No. 14 Texas A&M Saturday, puts Kansas State in position to assume the mantle in Sunday's Bowl Championship Series rankings.
The Horned Frogs (6-4, 3-4) were led by Trevone Boykin, who was limited to 17-for-31 passing for 169 yards, one touchdown and one interception.