Feldman (6-6) limited the Royals to two runs on six hits, walking one and striking out four as the Rangers took their fourth straight victory.
Josh Hamilton's two-run single in the third put Texas ahead to stay while Mike Olt added a pair of RBI as the American League West-leading Rangers clinched their three-game series.
Kansas City's Will Smith (2-4) absorbed the loss, surrendering four runs on eight hits over 5 2/3 frames.
Dog comes home gnawing on human bone
Julius Randle breaks leg during NBA debut