Blanco drew a two-out walk from Scott Linebrink (1-1), stole second and nabbed third base without a throw from White Sox catcher A.J. Pierzynski. Kendall then smacked a pitch into the left-center field gap, easily scoring Blanco with the winning run.
Kendall ended the day with two hits and a pair of RBI. Wilson Betemit socked a homer for the Royals, who took the rubber match of a three-game set at Kauffman Stadium.
Sean O'Sullivan (2-4) picked up the victory with a scoreless top of the 10th. Royals starter Zack Greinke went eight innings, yielding two runs on nine hits and striking out nine.
Pierzynski drove in a run for the Chisox, who started the day in second place four games behind the Minnesota Twins in the American League Central.