NEW YORK -- It wasn't until the White Sox returned to their Midtown hotel late Tuesday night that they heard about the first career walk-off home run allowed by Twins closer Joe Nathan against the Indians' Victor Martinez at Progressive Field.

The Twins' loss was a devastating one for the team, after Minnesota had fought its way back from an 8-7 deficit to take a 9-8 lead into the bottom of the eighth. It became doubly tough when factoring in Tuesday's setback as the sixth walk-off loss for Ron Gardenhire's crew since Aug. 10, with five coming since Aug. 26, coupled with the White Sox win at Yankee Stadium to increase their American League Central lead to 2 1/2 games and three in the loss column.

This combination of events gives the White Sox a little breathing room, at worst, with just 11 games remaining after Wednesday. And at the best?

Well, the White Sox could have their second division title in four years all but nailed down. Don't bother trying to convince the White Sox of that second option.

"Whether we are up three or they are up one or two, it's still going to come down to [next week's] series in Minnesota," White Sox reliever D.J. Carrasco said. "It will come down to us playing good ball and beating those guys at their place."

"We have to worry about them when we face them," added White Sox manager Ozzie Guillen. "Besides that, you wish they lose every game, but it's not going to happen. Every time we win and they lose, it's a little more air that comes through your lungs, that's it."

For about the past month, talk has focused on the three games between these two teams taking place at the Metrodome from Sept. 23-25 as the crowning moment of this division battle. But could the White Sox actually have this title in their collective sights before arriving in Minneapolis?

If the White Sox win three of their next five, as an example, including Wednesday's game, and the Twins do the same, the South Siders' magic number would be down to 5. Anything but a sweep at the hands of the Twins would seem to lead the White Sox into the playoffs.

Yet, don't look for any early acceptance of victory coming from the White Sox.

"A lot of people worry about the Minnesota series, but we got three vs. Kansas City and they play well against us," Guillen said. "We got to worry about Kansas City."

"It's going to come down to those three in Minnesota, like everyone thought, and we wouldn't have it any other way," White Sox catcher A.J. Pierzynski added. "Yeah, it's nice when we've won and find out they've lost, or on Sunday, we took the field and knew they lost that day. We knew we couldn't lose any ground, just pick up ground. So it's good, but at the same time, we know they will be there until the end, so we have to find a way to keep winning games."

Pierzynski knows the Twins' organization about as well as anyone on the White Sox, having played his first six big league seasons in Minnesota. He expressed respect held by the White Sox for their division rival, but also talked about his team being in a good position for these final 10 days.

"Coming out of Spring Training, if you told us that with 12 to go, we'd be 2 1/2 up, I'd take that," Pierzynski said. "I would much rather be in the Angels' position where they have it locked up and know where they are going. It works both ways."