Dunn was one of four Chicago players with three hits and one of nine White Sox who scored at least one run. Alex Rios also had a home run in his three-hit game and Eduardo Escobar scored three runs.
Chicago starter Chris Sale (9-2) took advantage of the support to pick up his sixth consecutive win. He allowed two runs and six hits over seven innings. He walked one and struck out five.
Twins starter Nick Blackburn (4-5), on the other hand, was rapped for six runs and nine hits in five innings. He allowed the home runs to Dunn, who is tied for the Major League lead with 24 home runs, and Rios, who has hit 10.
Rios doubled and scored in the second and new White Sox third baseman Kevin Youkilis doubled in Escobar in the third. Dunn chipped in a three-run home run in a four-run fifth that chased Blackburn.
Brian Dozer hit a Minnesota home run in the fifth but Dunn's RBI single capped a three-run Chicago sixth for a 9-1 lead.
The White Sox led by as much as 12-2 before Minnesota's Darin Mastroianni hit his first major league home run -- a two-run shot -- in the eighth and the Twins scored on a groundout in the ninth.
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