The Royals completed a 4-2 road trip, and stayed within four games of the Orioles for the American League's second Wild Card.
Kennedy improved to 11-9 with his 13th quality start. He gave up one hit, walked four and struck out six over six innings.
White Sox starter Chris Sale took the hard-luck loss, giving up two runs and eight hits over eight innings. Sale struck out 12, including striking out the side in the fifth to surpass 200 strikeouts. In doing so, he became the first pitcher in White Sox history to reach that milestone in four consecutive seasons.