Floyd (1-1) scattered seven hits and did not walk a batter, while striking out six. Bobby Jenks pitched a perfect ninth to record his 32nd save.
Magglio Ordonez homered to score the Tigers only run. Detroit has now lost five straight and 11 of their last 13 games.
Jordan Tata (1-1) managed to last only five innings against the White Sox, giving up three runs on five hits while walking four and fanning just two.
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