"It's all about Wang today," said Yankees manager Joe Torre. "Considering the fact that it was a close game, he was terrific. He got some good hitters out with men on base."
The Yankees staked Wang (2-3) to a lead in the third inning, scoring two unearned runs off Chicago starter Jose Contreras.
Derek Jeter reached on a one-out error and moved to second when Jason Giambi worked his second walk of the game. After Alex Rodriguez lined out, Matsui drilled a shot over the head of center fielder Darin Erstad, rolling to the wall and driving in both runners.
The play served as a great test for Giambi, who had returned to Los Angeles on the Yankees' off-day Monday to secure some custom-made orthotic inserts, hoping to cushion the slugger's ailing left foot.
As Giambi chugged on a 270-foot dash from first base to home plate, he didn't appear graceful, but Giambi rarely does. The most important thing, said Giambi -- who'd later single to end an 0-for-20 skid -- was that he felt little discomfort.
"That's the biggest thing, just getting some of the comfort back," Giambi said.
Meanwhile, Wang appeared plenty comfortable as he showed few ill effects from the issues that plagued his last start, an effort against Texas on May 10 that ended up as a 14-2 blowout loss.
Wang said he'd spent time in the bullpen working on his "smoothness" and it showed, as the right-hander had good control over a 91-pitch effort. Wang walked one and struck out three, keeping his fielders busy with the usual array of ground balls and a few more fly balls than normal.
"When you have Wang pitching like he was," Jeter said, "it makes you feel good."
Chicago finally broke through against Wang in the sixth, as Rob Mackowiak bounced a single up the middle, bringing home Erstad from second base.
But the Yankees escaped further damage in the inning as center fielder Cabrera fired to third base on the play, with Alex Rodriguez tagging out Pablo Ozuna in the basepath.
"Melky gives you a little shot of energy," Torre said of the 22-year-old Cabrera, who played both games of the doubleheader.
Limited to just three hits through the first six innings, the Yankees finally chased Contreras (3-4) in the seventh.
Bobby Abreu -- who had two hits, including a home run, in the first game of the doubleheader -- atoned for three strikeouts by stroking a two-out single to right, bringing in Cabrera.
Jeter followed with an RBI triple to right-center, staking New York to a three-run lead and eventually setting the stage for the Yankees' second victory in five games so far on this trip.
"We needed one of those games," Jeter said. "We need it to continue."
Contreras, who pitched for the Yankees in 2003 and 2004, was charged with two earned runs and five hits in 6 2/3 innings, walking three and striking out four. Cabrera and Posada added solo ninth-inning home runs off Andy Sisco.
Kyle Farnsworth retired the White Sox around two walks in the eighth inning and Mariano Rivera set down Chicago in the ninth.
The game, the second half of a doubleheader, was preceded by a rain delay of one hour and 15 minutes.
Torre said that even after the Yankees' 5-3 loss in the first game, their spirits remained loose and high -- infield coach Larry Bowa was said to have donned a batting helmet and volunteered to bat leadoff, an action the players found amusing -- and expressed optimism that the nightcap win could be the start of a roll for the Yankees, who improved to 18-20.
"We know we're better than this," Torre said. "We were probably a little tight [in the first game], but I felt pretty good."
Because Wang was efficient in his seven innings of work, Torre wouldn't rule out the thought that the right-hander could return on three days' rest to pitch against the Mets at Shea Stadium on Sunday.
Wang said he "maybe" could do it and said he'd accept the assignment if asked, but Torre said that would be a discussion to take place with pitching coach Ron Guidry in the morning hours.
"We'll do what we feel is best for him," Torre said.