Peavy (11-5), obtained from the White Sox in a July 31 trade-deadline deal, held his ex-club to five hits and a walk while striking out four.
It was the sixth win in seven games for American League East-leading Boston, which came into the contest with a 3 1/2-game bulge over second-place Tampa Bay.
Chicago's John Danks (4-11) was battered for six runs (five earned) on 11 hits over five innings.
Alejandro De Aza and Avisail Garcia each provided an RBI for the Chisox.
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