Sproles rushed for 92 yards and two touchdowns on 18 carries, raising his season total to 1,021.
The Walkers returned interceptions for scores in a 32-second span, igniting a 28-point third quarter. Kansas State (8-2, 4-2 Big 12 North) already had control of the game with a 30-7 halftime cushion.
The Wildcats, who have scored 166 points in their last three contests, kept alive their slim Big 12 title hopes, remaining one game behind Colorado.
A brutal schedule is proving to be Iowa State's undoing as the Cyclones (7-4, 4-3) have dropped three of four following a 6-1 start.
Prior to last week's overtime win over Missouri, Iowa State had suffered consecutive losses to Oklahoma and Texas. The difficult stretch continues next week with a contest at Colorado.