Chicago has taken the first two games of a three-game series against the first-place Royals.
After the White Sox captured Tuesday's series opener, Valentin led the way in the middle game by homering in his first three at bats. He hit a solo homer in the second, a three-run shot in the third and another solo blast in the fifth.
It was the second career three-homer game for Valentin.
After his third homer, Valentin walked in his next two plate appearances before striking out in the ninth.
Konerko added his fifth career grand slam for the White Sox, who produced their best offensive game of the season and closed within two games of the Royals.
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