Joe Adams scored on a 51-yard punt return and 16, in the Cotton Bowl.
Tyler Wilson threw two touchdown passes, including a 45-yarder to Jarius Wright that made it 19-0 in the second quarter, and Arkansas (11-2) tied a school record for wins in a season.
The Razorbacks' only losses this season came to the country's two best teams, SEC foes LSU and Alabama, who will meet in the BCS National Championship Game on Monday.
Kansas State scored nine quick points before halftime, cutting the Arkansas lead to 10 on a blocked extra point return and Collin Klein's short touchdown pass to Andre McDonald.
The Wildcats (10-3) were within three points in the third quarter, but didn't score again and had a three-game winning streak snapped to end the season. They dipped below .500 in 13 bowl games under head coach Bill Snyder.