Greinke allowed two runs, two hits and a walk in five innings today, striking out three in Kansas City's 4-to-3 victory over the Chicago White Sox.
Greinke is competing with Brian Bannister for the only remaining vacancy in the rotation.
Greinke has put together consecutive solid starts, pitching four scoreless innings against Colorado in his previous outing.
White Sox starter Adam Russell held the Royals to five hits and one run over four innings, walking two and striking out four.
Brian Anderson homered in the eighth for the White Sox off left-hander Jimmy Gobble to tie the score at 3. Juan Uribe had an inside-the-park homer in the second.
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