Santana (4-5) logged his first victory since April 27, a span of six starts. The veteran right-hander yielded five hits without a walk and struck out six.
Salvador Perez and Eric Hosmer each drove in a run in the first inning for a quick Kansas City lead. Lorezno Cain added two RBI as the Royals clinched their three-game series.
Houston's Erik Bedard (1-3) was charged with the loss, surrendering six runs on eight hits over 4 2/3 frames.
Chris Carter socked a solo homer for the Astros.