MINNEAPOLIS -- This game could have and should have been a momentum-changing victory for the White Sox in the chase for the American League Central title.

Tuesday's series opener at Target Field with the Twins could have been the kind of win the White Sox looked back on in October and said, "That's where the division was won."

Instead, this ballgame turned into a 10-round heavyweight battle, with Jim Thome delivering the knockout punch in a 7-6 Minnesota victory before the 55th sellout this season for the Twins.

And when Thome's prodigious clout off Matt Thornton (3-4) landed in the right-field stands with nobody out in the bottom of the 10th inning, it just might have been the blow making it tough for the White Sox (65-54) to get up off the 2010 canvas.

Even with 43 games remaining, including five against the Twins (69-50), and with just a four-game deficit staring them in the face.

That sense of urgency is not lost on the South Siders.

"We just have to go out and play," White Sox catcher A.J. Pierzynski said. "We know what we have in front of us. If we go out and play like we're capable of, things will work out."

"It isn't going to be easy," said White Sox starting pitcher John Danks, who finished with a no-decision Tuesday after giving up five runs on 11 hits over seven innings. "Hopefully we can win a couple and make it a two-game deficit. We are not going to give up. We will play until we are told we are not there anymore."

When Danks talked about things not being easy, he was referring in the short term to the White Sox facing Francisco Liriano and Carl Pavano during the next two games in Minneapolis. Danks could have been talking about catching the Twins, in general.

The White Sox spotted Ron Gardenhire's crew a 4-0 lead in the first and needed an Alexei Ramirez home run leading off the ninth against Minnesota closer Matt Capps to force extra innings. Three straight singles from Mark Kotsay, who homered among his three hits, A.J. Pierzynski and Ramirez broke the tie against John Rauch in the 10th, but the White Sox stranded two more runners.

They also failed to score with the bases loaded and one out in the ninth, when Paul Konerko, who launched his 30th home run earlier in the evening, hit into an inning-ending double play. All of these occurrences set the stage for the Thornton-Thome matchup, following Delmon Young's leadoff single.

Thome entered hitting .250 against southpaws. Left-handed hitters were 13-for-82 against Thornton this season.

Advantage, Thornton. Win to Thome for career home run No. 581.

"In moments like that, you want to try to be in that situation," said Thome, who hit his 43rd career home run against the White Sox and the first walk-off hit at Target Field. "You are not going to do it all the time. With Thornton, he's one of the best left-handed relievers in the game. It worked out great."

"I don't care who hits a home run," said Thornton, who was in his third inning of relief. "We lost the game. The fact is our offense battled all night. We got down four early, we scored three to come back and picked away. Tied in the ninth, went ahead in the [10th]. That's the only thing that hurts for me."

While the late White Sox rally officially started in the ninth, the seeds of the comeback were planted in an eighth-inning exchange befitting this intense rivalry.

With runners on second and third and one out, reliever Sergio Santos came in high and tight on J.J. Hardy and almost hit Hardy in the head. That pitch brought out Minnesota manager Ron manager Ron Gardenhire for a discussion with home-plate umpire Bill Hohn. Gardenhire may have had in the back of his mind last week, when the White Sox thought that Glen Perkins threw intentionally at Carlos Quentin at U.S. Cellular Field.

Santos spoke more about missed location on this particular pitch.

"I'm trying to go low and away and it just kind of went up and in," said Santos of the pitch to Hardy. "Luckily I was able to regroup and throw a strike."

Hardy grounded Santos' strike to second baseman Gordon Beckham as part of a drawn-in infield, and when Beckham threw home to nail Young at the plate, Young appeared to take a upper-cut to the face of catcher Pierzynski, without making much of an attempt at reaching the plate. The White Sox looked revitalized in the ninth, although not much was made of the play publicly following Thome's shot.

"He did what he needed to do," said Pierzynski of Young's play. "It was a play at the plate. Things happen and you move on."

"I was so hosed," Young said. "I couldn't slide."

A loss such as this one is tough enough for the White Sox to take at face value. Add in a third straight loss for the team when leading in the eighth inning or later and the fifth of the second half.

Top it off with the walk-off culprit being Thome, a highly respected individual in White Sox circles, but also a player the team decided not to bring back for 2010 in looking at a more athletic, versatile use of the designated hitter spot. That combination makes the tough fight talked about by Danks seem almost impossible.

Regardless of the appearance, the White Sox won't give up.

"There's nothing you can do about it," White Sox manager Ozzie Guillen said. "[The Sox players] have two huge games to play and if they play the way they did today, I will take my chance."