With manager Joe Girardi back on the bench following an illness, Chamberlain and second baseman Robinson Cano got the Yankees out of a dicey jam in the seventh. Rivera recorded three quick outs in the ninth, and New York won for the third time this year when scoring three runs or fewer.
The Yankees were 6-36 in such games last season.
"You're going to have those weeks," Girardi said. "We got enough today and that's what matters. This offense will break out."
Tampa Bay, which was looking for the best five-game start in its 11-year history, dropped to 3-2 after winning the first two of the four-game series. Girardi missed those games because of an upper respiratory infection while bench coach Rob Thomson managed in his place.
"Nice being back on the bench," said Girardi, adding that his fever was gone. "It's nice being out in that fresh air. Even though it's chilly, you just feel better when you're out there."
Matsui homered in the fourth off James Shields and finished with three hits. The Yankees (3-3) have scored only 17 runs this season -- no more than four in any game.
"Hopefully, you'll see a lot more hitting from us," Johnny Damon said. "We plan to score some runs here soon."
Pitching in short sleeves on a 46-degree afternoon, Wang (2-0) held the Rays hitless until the fifth and took a two-hitter into the seventh.
Cliff Floyd and Eric Hinske opened the inning with singles, putting runners at the corners. Girardi brought in Chamberlain, who soon hit 101 mph on the stadium radar gun and struck out Willy Aybar on three pitches.
Shawn Riggans followed with a line drive that appeared headed for center field, but Cano made a backhand stab and doubled up Hinske at first base after he wandered too far off the bag.
"It was a little different coming in with runners on base, but it was good to do that," Chamberlain said. "You don't want to give up the runs for Chien-Ming. He did such a great job. The bullpen's got to hold it down."
Also working in short sleeves, Chamberlain tossed a perfect eighth before Rivera fanned two in a 1-2-3 ninth. The Yankees are 20-2 in regular-season games when Chamberlain pitches. He has set up Rivera for a save in all three New York wins this season.
"There's definitely an energy when he comes in," Girardi said.
A trainer came out to check on Wang after he appeared to slip on the mound in the fourth. He stayed in the game, however, and finished with six strikeouts.
"He's the No. 1 guy over there for a reason," Riggans said. "He threw the ball excellent, moved it around, changed speeds. Then you get Chamberlain and Rivera."
Wang, known for his nasty sinker, mixed in his slider, splitter and changeup effectively.
"I'm trying to find more ways to get hitters out. I don't want to rely on just my sinker," he said through a translator.
After beating Baltimore 6-2 on opening day, Shields (1-1) gave up eight hits in five-plus innings, struck out five and walked one.
Alex Rodriguez doubled with one out in the fourth, and Matsui followed with a shot to right, his second homer in three games.
"I made one bad pitch. I hung a changeup to Matsui and he hit it out. I got outpitched today," Shields said. "Today was a day when you've got to shut them down. Wang out there, he pitched great today. That was the game, that one pitch."
Matsui, moved up to fifth in the lineup Sunday, is 6-for-10 against Shields with three homers and a double. The slugger had a chance for a huge day, but struck out with the bases loaded, ending the fifth.
Aybar singled with one out in the fifth for Tampa Bay's first hit, and an error by Cano left runners at the corners. But Jason Bartlett missed on suicide squeeze attempt, making Aybar an easy out when catcher Jorge Posada chased him down. Bartlett then struck out, ending the inning.
"That was a mis-assignment. That was a Rays mistake. We messed it up," manager Joe Maddon said. "It wasn't supposed to happen the way it happened."
Rays center fielder B.J. Upton made a diving catch in the first and a strong throw to cut down Wilson Betemit when he tried to go from first to third on Melky Cabrera's single with none out in the third.
- Yankees 1B Jason Giambi sat out with a sore left groin.
- Cabrera returned from a two-game suspension for his role in a spring training fight with the Rays. Yankees backup 1B-OF Shelley Duncan began serving his two-game suspension for his part in the scuffle.
- Rivera didn't get his third save last year until May 3.