The American League Central standings probably seemed like an optical illusion for Twins fans Tuesday morning.

Were the downtrodden Twins really sitting 7 1/2 games out of first place? Could they really trim that margin to 5 1/2 games with two more victories over the White Sox this week?

Yes and yes, but this was mostly an indictment of the AL Central.

The reality check came later in the day, as the Twins flailed away against Gavin Floyd for seven innings before a ninth-inning rally fizzled in a 3-2 loss to Chicago at Target Field.

Jamey Carroll's two-run single with two outs in the ninth made things interesting, but with the potential tying and winning runners on base, White Sox closer Addison Reed got Denard Span to ground out to second base, ending the game.

"We finally had some quality at-bats there at the end," Twins manager Ron Gardenhire said. "... We had a chance, and unfortunately we came up a run short."

No matter what the games- behind column of the standings says, these are the hard facts: The Twins are in last place, 13 games under .500 and sitting behind four less-suffering teams. To win this series against Chicago on Wednesday, they will have to overcome lefthander Chris Sale, who leads the AL with a 2.24 ERA.

The Twins better be more opportunistic. Floyd (6-7) racked up nine strikeouts and held the Twins to five hits over seven scoreless innings. The big righthander was 0-8 in eight previous starts against Minnesota and had struggled against several teams before pitching 6 1/3 scoreless innings against the Cubs last Wednesday.

The Twins had chances against Floyd, especially early, but went 0-for-8 against him with runners in scoring position. Joe Mauer, who had reached base in a remarkable 15 consecutive plate appearances against Floyd dating to 2010, picked a bad time to end that streak, striking out with one out and a runner on third base in the first inning.

Floyd also struck out Mauer looking in the third inning with a runner on second.

"This game is about pitching and about timely hitting," Carroll said. "[Floyd] won those battles tonight. I know I had a chance with a couple runners on in my first at-bat, and he threw a pitch to me that I thought was a fastball, and it was a slider. And he kept doing it to me all night."

Twins starter Liam Hendriks fell to 0-5, giving up three runs on five hits over 6 1/3 innings. He showed progress, lowering his ERA from 7.39 to 6.82, but the 23-year-old from Australia has now made 11 major league starts without getting a victory.

"Eleven and counting," Hendriks said. "Still looking for that No. 1, but it'll come. I'm not too worried about it."

It could have come this time if he had received some offensive support. The White Sox broke the scoreless tie in the fourth, as Paul Konerko drew a one-out walk and Alex Rios followed with a two-run homer into the second deck in left field.

With a 1-0 count, Hendriks threw a hanging slider and shouted at himself after the ball left Rios' bat. Hendriks quickly composed himself, retiring Chicago's next eight batters before the White Sox scratched out another run in the seventh.

Pulled from the game, Hendriks received good ovation as he walked off the mound, trailing 3-0, but that didn't help the win column -- for him or the team.