Kluber (2-4) notched his second major league victory, allowing four hits and three walks while striking out four en route.
Francisco Liriano (6-12) was roughed up for four runs on seven hits in a 3 2/3-inning effort for the American League Central-leading White Sox, who fell for the sixth time in seven games and saw their lead over the Detroit Tigers shrink to one-half game.
A.J. Pierzynski and Dayan Viciedo hit back-to-back homers in the fifth for Chicago.
2014: NFL Cheerleaders [PHOTOS]
Michael Sam cut from the Dallas Cowboys