Klein threw one TD pass and ran for three scores for Kansas State (2-0), which out-gained the Hurricanes (1-1) in total yards 499-264.
Klein finished 9-of-11 for 210 yards and ran 22 times for 71 yards in the Wildcats' 11th consecutive home win against unranked opponents.
John Hulbert ran for 106 yards and a touchdown for K-State and Tyler Lockett caught three passes for 59 yards.
Miami's Stephen Morris was 19-of-26 for 215 yards, but the Hurricanes were 5-of-13 on third-down conversions and averaged 1.6 yards per carry on the ground.
Kansas State ran up a 24-6 halftime lead and tacked on 21 points in the fourth quarter to put the game out of reach.