The free-agent catch gave them that -- and more -- Tuesday night, flirting with a no-hitter before settling for a 7-2 victory over the AL champions that kept him unbeaten since signing an $82.5 million, five-year deal.
"I had good movement on everything. I was putting the ball where I wanted," Burnett said after taking his no-hit bid into the seventh inning. "It definitely could have happened. But it wasn't meant to be."
Mark Teixeira, another of the Yankees' high-priced offseason acquisitions, drove in the go-ahead run with an eighth-inning sacrifice fly off J.P. Howell (0-1) after missing New York's previous three games with tendinitis in left wrist.
Derek Jeter added a three-run homer in the ninth for the Yankees, who were humbled 15-5 on Monday night.
The Rays added a second run in the inning on Pat Burrell's sacrifice fly to make it 2-all heading into the eighth, when the Yankees broke the tie with a double, single and Teixeira's sacrifice fly.
"Sac flys aren't sexy, but they get the job done," Teixeira said.
Burnett allowed two runs and three hits, walked one and struck out nine in eight innings -- taming a torrid offense that had 17 hits in each of its previous two games, scoring 26 runs in victories over Baltimore and the Yankees.
"You're not going to score 10-plus runs every night," Rays manager Joe Maddon said. "We made a charge toward the end ... but couldn't get it done."
Jorge Posada had a bases-loaded sacrifice fly off Matt Garza in the first inning. Swisher, obtained from the Chicago White Sox in an offseason trade, added a solo homer in the fourth before Garza settled down to keep the Rays in the game.
Jeter finished 3-for-5, and his 208th career homer tied him with Alex Rodriguez for 11th on the Yankees' list. Right fielder Xavier Nady left after the seventh inning with a sore right elbow and will have an MRI exam Wednesday.
A night after raising the first division and league title banners in franchise history, the Rays received 14-carat white gold AL championship rings featuring 48 diamonds during a pregame ceremony.
But unlike Monday night, when they got off to a fast start with four runs in the first inning and five more in the second, the Rays only managed to get three balls out of the infield before Crawford lined his opposite-field single leading off the seventh.
"He did a good job of not giving us anything over the plate to hit," said Evan Longoria, who followed with a single. "He was throwing 95 [mph] on the corners. That makes it difficult."
Burnett threw a no-hitter for the Florida Marlins on May 12, 2001, at San Diego but maintains he's still somewhat embarrassed by the accomplishment because he walked nine that day -- most ever in a no-hitter.
"That was a long time ago. I didn't know where the ball was going then. Plus, I only threw one pitch pretty much," the right-hander said. "I've always had a goal to throw another one so I can wipe that one away."
Burnett started thinking about the possibility in the third inning. His teammates thought he had a good chance, too.
"He was awesome," Teixeira said. "In the back of my mind, I'm saying 'I know he's done it before, and he can do it again.' Guys just didn't look comfortable against him tonight. He had great stuff."
Garza, who beat Boston and Jon Lester in his first start of the season, struck out nine and walked two while allowing two runs and five hits in seven innings. ... Rodriguez, rehabbing from hip surgery, worked out again at the club's complex in Tampa. He expects to begin taking batting practice soon. ... Rays SS Jason Bartlett homered Sunday and Monday, doubling his total from last season when he hit one in 454 at-bats. ... Including the postseason, the Rays have sold out 12 consecutive games at Tropicana Field. It's the first time they've sold out the first two games of a season. ... New York finishes its nine-game, season-opening road trip Wednesday, and the new Yankee Stadium opens Thursday. Longtime public-address announcer Bob Sheppard will not work the home opener while he continues to recover from a bronchial infection. Sheppard, who missed last season because of his illness, became the voice of the old Yankee Stadium in 1951. ... According to the St. Petersburg Times, Longoria will miss Wednesday's series finale and likely Thursday's game against the White Sox to return to California to attend to what a team official described as a family matter.