Adam Dunn and Conor Gillaspie added two solo home runs in the ninth inning but it proven to not be enough to overcome the Twins five run lead.
In the fifth inning, Twins second baseman Brian Dozier broke the scoreless tie with a three-run homer and All-Star catcher Joe Mauer added a two-run homer.
Sox starter Jose Quintana (6-3) and Twins right hander Kevin Correia (7-8) battle through four scoreless innings to start the ballgame.
Alejandro De Aza doubled to lead off the third but was thrown out trying to advance to third on a ground ball to short by Gordon Beckham. De Aza failed attempt marked the 21st time this season he has been thrown out, including caught stealing.
Quintana allowed five runs on six hits and struck out six in five innings pitched. Correia threw seven innings, giving up five hits and striking out seven.
Sox ace pitcher Chris Sale (7-11) and Detroit Tigers Doug Fister (10-5) are the projected starters for the opening game of a three-game home series for the Sox at 7:10 p.m. CT (CSN, WSCR 670).