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"I found my closer -- Lillibridge," Guillen said. "We know he can play the outfield really well."
Lillibridge stayed in the game in right field and, with two on in the ninth, raced back to the wall to make a terrific catch of Alex Rodriguez's opposite-field drive for the second out, robbing the slugger of a game-tying hit and keeping the runners at first and second.
Robinson Cano then hit a line drive to right and Lillibridge charged in, making an all-out dive to snag the ball just inches off the grass for the final out.
"We needed a break like that," Lillibridge said. "I'm glad he feels comfortable with me out there. I've always felt a part of this team."
Floyd was already looking forward to watching the highlights on television.
"Better be 1 and 2 on webgems tonight," he said.
Guillen, still looking for a reliable closer in his shaky bullpen, called on Sergio Santos for the second consecutive night. He got two outs -- thanks to Lillibridge -- for his second straight save and Chicago's third in nine chances this season.
"I haven't felt that alive in a long time," Santos said. "I haven't yelled that loud in my life -- ever."
The last visiting pitcher to win at the old Yankee Stadium in 2008, Floyd (3-1) struck out a season-high 10 to win his second straight start. He walked one and threw 102 pitches, sending the White Sox to consecutive victories in New York for the first time since August 2005.
Before arriving at Yankee Stadium, they had lost 10 of 11 overall.
Cano and Brett Gardner homered for the Yankees, held to three singles by journeyman Phil Humber and two relievers during a 2-0 loss in the series opener Monday night. This time, they wasted a strong start by rookie Ivan Nova, who left with a 2-1 lead after a career-high 6 1/3 innings.
New York, now 18-5 following shutout losses since the start of the 2008 season, has lost two in a row for the first time this year.
"Two incredible plays. Very courageous dive, because if the ball tips off his glove, the game's over," Rodriguez said.
"Bad month," Soriano said. "I'll take it and come back next month."
After saving an AL-best 45 games for Tampa Bay last year, Soriano signed a $35 million, three-year contract with the Yankees in January to be the bullpen bridge -- and possible successor - to star closer Mariano Rivera.
But the right-hander has a 7.84 ERA in 11 appearances and was booed Tuesday night by the crowd of 40,785. He has given up nine earned runs in 10 1/3 innings after yielding only 12 all last season.
"I still believe he's going to be very, very good for us," manager Joe Girardi said. "I haven't lost my confidence in Rafael Soriano.
"Tonight's the best his velocity has been. He just made a mistake to Konerko," the manager added. "Let's not forget he closed out 45 games last year in a tough division. I haven't seen anything that tells me he can't handle New York."
The Yankees had three chances to retire Alex Rios in the fifth and never did it.
Granderson was unable to make a shoestring catch on Rios' line-drive single to center. Rios then stole second, catching a break when Cano dropped a strong throw that could have been in time. Finally, Rios slid home ahead of the throw from right fielder Nick Swisher on Gordon Beckham's RBI single.
Nova set down Brent Morel and Juan Pierre to minimize the damage. The right-hander, who beat Floyd 2-1 last August for his first career win, allowed five hits in his first start since April 15. It was the longest of his 11 major league starts.
- Before winning the first two games of the series, the White Sox were 0-11 when scoring three runs or fewer.
- Chicago LHP Mark Buehrle makes his fifth attempt at career win No. 150 on Wednesday night. RHP Bartolo Colon pitches for the Yankees. He beat Toronto 6-2 last Wednesday in his first big league start since 2009.
- Guillen said DH Adam Dunn could begin seeing time at first base on the team's next homestand.