Down 1-0, it all turned promising in the fourth as the Sox chased Mays from the game with five runs on six hits and a walk.
Willie Harris and D'Angelo Jimenez started things off with singles, and Frank Thomas walked to load the bases, setting up a RBI-single by Brian Daubach. Carlos Lee, who left six men on base total, grounded into a fielder's choice forceout at second, scoring Jimenez from third.
Jose Valentin put the Sox up 5-1 with a three-run homer to right, but two singles, one out and a walk later ended with Jimenez striking out.
The defense then kicked in for the Sox in the fourth as Torii Hunter reached on a throwing error by Joe Crede and two batter's later on a double by AJ Pierzynski.
Garland didn't last much longer, getting pulled with two outs, a run in and two men on in the sixth. Damaso Marte came in and gave up the game-tying two-run double by Jacque Jones, who later inflicted the final damage with the game-winning homer in the 11th.
In 5 2/3 innings, Garland struck out two and walked two, giving up nine hits and allowing five runs (four earned) on 93 pitches.
After the fourth, the White Sox were shutdown by the Twins' bullpen, failing to score on a first and second situation in the seventh and a bases-loaded, one out opportunity in the ninth.
Lee and Valentin ended the threat with a strikeout and popout respectively, making the baserunning blunder by Jimenez -- one in which he misread a softly hit single by Ordonez, only advancing to third from second -- that much bigger.
Marte went on to throw 2 1/3 scoreless innings, while Tom Gordon followed that up with two scoreless innings of his own. Billy Koch started the 11th inning, and after retiring the first batter, gave up the homer to Jones.
The White Sox will now hope to take the final game of the series with a win on Thursday afternoon at 12:05 CT. Mark Buehrle is scheduled to pitch against Brad Radke. The game will be televised on Fox Sports Net Chicago.