Houston were first to get on the scoreboard at the Arrowhead Stadium, with Randy Bullock making a 48-yard field goal.
Kansas responded with a sustained drive up field, which led to Jamaal Charles crossing the line from close range for the opening touchdown.
Houston came roaring back and scored a touchdown of their own with the first play of the second quarter, as Keenum found DeAndre Hopkins with a precise 29-yard pass.
With time running out in the first half, Kansas got into a scoring position thanks to patience from Smith, with the quarterback finishing things himself by finding the end zone to give the Chiefs a four-point lead at the half.
Bullock and Ryan Succop then traded field goals, before a third Texans field goal moved the visitors to within a point late on.
Houston then lost linebacker Brian Cushing to a leg injury as their injury problems piled up, but won back possession with less than two minutes left.
With the pressure on, Kansas used their fierce defence to force an error, with Tamba Hali stripping Keenum of possession as the Chiefs closed out their seventh straight win.