Heisman Trophy candidate Klein (8-of-14, 184 yards) passed for a pair of scores and also scored twice on the ground while running for 103 yards on 23 carries.
John Hubert scored three times en route to 66 yards on 14 carries, while Tyler Lockett made two receptions for 73 yards and a touchdown for the Wildcats (11-1, 8-1 Big 12).
Kansas State will get the BCS bowl bid despite ending the season tied with Oklahoma atop the Big 12 thanks to its 24-19 win over Sooners in September.
The Longhorns (8-4, 5-4) got a big performance from Case McCoy, who amassed 314 passing yards and two touchdowns while subbing for David Ash, but it wasn't enough to secure a win.
Swim Week Miami Beach 2014 [PHOTOS]