The Twins remained 2 1/2 games behind Detroit in the divisional race. The Tigers beat Cleveland earlier Tuesday.
Paul Konerko, Gordon Beckham and Alex Rios homered for the White Sox, who have lost six of their last seven games. John Danks (12-10) suffered the loss after he surrendered seven runs on eight hits over six innings.
Jesse Crain (7-4), who pitched 1 1/3 scoreless relief innings, earned the win while Joe Nathan pitched a perfect ninth for his 43rd save of the season.
Copyright 2009 by United Press International.