Iowa State suffered a 38-31 loss to Florida State last week when quarterback Senecca Wallace was stopped on the one-yard line on the final play of the game.
Wallace completed 16 of 24 passes for 234 yards against the Jayhawks (0-1, 0-1 Big 12 North), who allowed 511 total yards.
The Cyclones (1-1, 1-0) scored all six of their touchdowns on the ground. Brian Thompson ran for 92 yards and two scores on 14 carries while Michael Wagner also scored twice and wide receiver Lane Danielson once on a reverse.
Danielson's nine-yard touchdown gave Iowa State a 10-0 lead with 3:57 left in the first period before Rutland's seven-yard score with 90 seconds remaining in the second helped the Cyclones to a 17-0 halftime advantage.
Wagner's six-yard run made it 24-0 before Kansas got on the board on Johnny Beck's 28-yard field goal as time expired in the third quarter.
The Cyclones broke it open it with 17 unaswered points in the final period. Wagner scored on a six-yard run before Thompson reached the end zone on runs of seven and 15 yards.
Kansas managed just 150 total yards. Bill Whittemore completed a mere four of 17 passes for 31 yards before giving way to Zach Dyer.
Clark Green was Kansas' leading rusher with 31 yards on nine carries.