TCU (16-10, 3-10 Big 12) never trailed in the game, but had to hold on after building a 35-15 halftime lead that was bolstered by a 19-0 run over the final 7 1/2 minutes before the break.
This is the third Big 12 season for the Horned Frogs, who went 0-18 in league play a season ago after a 2-16 debut in 2013. They were coming off a 70-55 home win over No. 22 Oklahoma State four days earlier.
Kansas State (13-14, 6-8) scored 11 consecutive points in less than two minutes early in the second half. The Wildcats got as close as 41-35 when Nino Williams made a free throw after a technical foul against TCU with 11:52 left.