Alfredo Aceves (9-1) provided stellar relief following an abbreviated outing for Chamberlain. With the Yankees determined to limit his workload, the 23-year-old right-hander was pulled after only three innings and 35 pitches.
"It's good that we're winning. Because I'm sure if we weren't playing well and we weren't winning, then people would make a bigger story out of it," Derek Jeter said. "But you have to realize that Joba hopefully is going to be here for a long time, so in the same sense you want to make sure that he's healthy."
Jeter scored three times for the AL East leaders, who boosted baseball's best record to 82-48. They are 31-11 since the All-Star break, also the top mark in the majors.
"Well, we came to New York and visited the new Yankee Stadium. It is a very nice ballpark, and the hotel we stayed at was also very nice," manager Ozzie Guillen said. "That's all I have to say about these last three days."
Up next, a three-game series at AL Central rival Minnesota. It will be Chicago's final visit to the Metrodome, where the White Sox are 2-14 in their past 16 games and 88-112 overall.
"I think the next three games, we're in or we are out," Guillen said. "We have to win the series out there, there's no doubt."
While the White Sox are fading in the playoff race, Teixeira is making a push for AL MVP honors. The switch-hitting slugger, in his first season with the Yankees after signing a $180 million, eight-year contract, has 32 homers and 101 RBIs.
He's reached 30 home runs and 100 RBIs for six straight seasons, joining St. Louis star Albert Pujols as the only major leaguers to accomplish the feat.
Damon's two-run shot off Freddy Garcia (0-2) in the third gave New York a 3-2 lead, but Chamberlain never got a chance to hold it.
"You've got to realize what they're trying to do -- to protect me for a long time," Chamberlain said. "It's humbling for me to know that they care that much about me. ... I feel good, but I also understand this is a process."
The Yankees broke it open against Chicago's bullpen in the bottom half, highlighted by Melky Cabrera's RBI double off the left-field fence and Teixeira's high drive that cleared the short porch in right.
Aceves entered in the fourth and pitched three scoreless innings of two-hit ball to earn the victory. The versatile right-hander has nine wins out of the bullpen, most among big league relievers.
"He's been huge. As a reliever, nine wins, that's incredible," Teixeira said. "Very flexible. Whatever you need from Ace he's going to give it to you."
The White Sox lost 10-0 on Saturday, when they made three errors and managed one hit against Sergio Mitre and Chad Gaudin. After that one, Guillen said everyone in his clubhouse "should be embarrassed." He mixed in a few expletives, but never shouted.
Before the series finale, Guillen offered similar comments.
"As a group, we all stink right now," he said, adding that the only two members of the White Sox currently earning their paychecks are the trainers.
Jeter singled with two outs in the third and Damon drove the next pitch deep into the second deck in right. It was Damon's 24th home run, matching the career high he set in 2006 with the Yankees.
"We have such a great team from top to bottom," Damon said.
Damon came out in the seventh with cramping in both calves. He was pulled for pinch-hitter Jerry Hairston Jr., who delivered a bases-loaded sacrifice fly.
"I'm expecting to play tomorrow," Damon said.
Teixeira also had a sacrifice fly, in the first.
C Jorge Posada returned to New York's lineup after missing three games with a bruised left ring finger. He went 2 for 3 with a double and a walk. ... White Sox 1B Paul Konerko was rested. Mark Kotsay started at first base. ... Damon's homer was the 200th at the new Yankee Stadium.