KANSAS CITY, Mo.—Mark Buehrle was dominant into the ninth inning, allowing six hits and a run, and the surging Chicago White Sox beat Kansas City 4-1 Thursday night for their fifth victory in a row.

Now 20-8 lifetime against KC, Buehrle started the ninth with a four-hit shutout but failed to get his first complete game since May 2, 2008, when Alberto Callaspo doubled and scored on David DeJesus’ one-out double.

He was relieved by Bobby Jenks, who got the last two outs for his 19th save in 21 chances for the White Sox, who have won 10 of their last 12 games and 14 of the...

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