Peavy (5-1) allowed two runs on five hits and struck out six in Chicago's second win in their last three games.
The White Sox scored twice in the eighth inning to break a 2-2 tie. Addison Reed pitched a scoreless ninth for his 12th save.
Kevin Correia (4-3) took the loss for the Twins, who dropped their third game in five tries. Trevor Plouffe and Oswaldo Arcia drove in Twins' runs.
Aaron Carter is still in love with Hilary Duff
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