Samuel Deduno's wild pitch allowed Chicago's Leury Garcia to score the game-winner.
It was a rough 11th inning for Deduno, who made his bullpen debut for the Twins. A bunt single, a pair of wild pitches, and a balk doomed the Twins righty.
The Twins had their chances to win the game before it went into extra innings, but a blown save from Glenn Perkins in his first appearance of the season and an error from Trevor Plouffe in the ninth allowed the White Sox to score a pair of runs and erase a 6-4 Twins lead.
Minnesota trailed most of the day, but a three-run seventh inning put the Twins on top and in position to pick up the win.
Plouffe and Kurt Suzuki put together three-hit games. Plouffe was 3-5 with 3 RBI. While Suzuki was 3-6 with an RBI to lead the Twins. Jason Kubel made his first start in his return to the Twins. Kubel didn't disappoint, he finished 2-6 with a pair of doubles and an RBI.
For the second straight game Aaron Hicks had a pair of hits.
Kevin Correia started on the mound for the Twins. He gave up three runs (two earned) on five hits while striking out five, in six innings.
The game featured Ron Gardenhire's first successful replay challenge. Oswaldo Arcia lifted a fly ball to center field that Eaton appeared to catch but bobbled and dropped as he tried to grab the ball from his glove.
The play was originally ruled a catch, but Gardenhire challenged the play and it was overturned after a review. The overturned call allowed Plouffe to advance to second even though he never tried to go on the fly ball, which he believed was caught.
The Twins (0-2) and the White Sox (2-0) play the final game of their series on Thursday.