John Hubert rushed for 157 yards and a touchdown on 23 carries for Kansas State (5-4, 3-3 Big 12).
The Wildcats gained 291 yards on the ground to 105 for Texas Tech (7-3, 4-3).
Freshman quarterback Davis Webb completed 13-of-20 passes for 77 yards for Texas Tech, before being replaced in the second quarter by Baker Mayfield, who threw for 265 yards and a TD but also turned the ball over three times.
Kansas State led 35-10 at halftime and scored 14 points in the fourth quarter on a 1-yard TD run by Sams and a 43-yard interception return by Tyler Zimmerman.
The victory made Wildcats Coach Bill Snyder the 11th coach in FBS history to win 175 games with the same school.