Miller, who threw for two touchdowns and ran for one, was perfect on five fourth-down conversions and nearly as flawless passing for the Wildcats, 6-0 overall and 2-0 in the Big Eight.
He was 17 for 21 for 261 yards, including an 18-yard touchdown pass to Brian Lojka with 5:29 remaining for the go-ahead score. It came one play after Miller ran three yards on fourth down at the 21.
The victory keeps Kansas State perfect heading into next week's game at No. 2 Nebraska (6-0, 2-0).
"Sometimes we're good enough to get it done," Snyder said. "I hate like the devil to say it because I don't want our players to believe it. We're going to have to be as good a football team as we conceivably can be" to beat Nebraska, which beat Missouri, 57-0.
The Cowboys (1-5, 0-2), got 181 rushing yards from David Thompson.