NEW YORK -- Derek Jeter didn't waste any time after he homered in the fifth inning Sunday. He quickly traded a bat and a ball for a reminder of the day he tied Lou Gehrig for the most hits at Yankee Stadium.
"It's definitely special," he said.
The Rays went 3-6 on their 10-day trip to Toronto, Boston and New York and will carry a one-game lead into their three-game series against the second-place Red Sox beginning Monday night in Florida.
"It's never good to lose a series," manager Joe Maddon said. "It was obviously a tough road trip ... not easy at all. The Yankees are one team that we haven't played well against this year."
Jason Giambi hit a two-run homer for New York, still clinging to faint playoff hopes during its final homestand at its longtime ballpark.
Mariano Rivera entered with two on in the ninth and struck out Erick Aybar for his 35th save in 36 opportunities. The All-Star closer also moved into a tie with Lee Smith for second on the career list with 478 saves.
"I'd rather have the team, our team, tied for first place," Rivera said.
Fernando Perez, who went to nearby Columbia University, hit a three-run drive for Tampa Bay, which started the trip with a 3 1/2-game lead in the East.
Oft-injured Yankees pitcher Carl Pavano (3-1) allowed three earned runs and five hits before he was booed off the mound in the sixth inning following a visit by the trainer and manager Joe Girardi.
Pavano was pitching to Eric Hinske with one out and a runner on first when he got the mound visit. After a short discussion, the right-hander walked off as the sellout crowd, familiar with his injury history, showered him with boos.
"I'm at a spot right now where I'm starting to wake up muscles I haven't used in a while," said Pavano, who left with a stiff left hip and expected to be OK for his next start. "Every time I go out there, there's more innings than the last time and more pitches than the last time so I mean these are things I'm going to have to work through."
Pavano has started only 24 games for the Yankees since signing a four-year, $39.95 million contract before the 2005 season.
"He did not want to come out," said Girardi, who opted for the safe route on a muggy day in the Bronx. "He told me he was fine."
David Price, the top overall pick in the 2007 draft, made his major league debut for Tampa Bay and threw 5 1/3 impressive innings in relief of struggling starter Edwin Jackson. The 6-foot-6 left-hander allowed two runs and three hits, spending much of the outing in the upper 90s.
"It was fun," he said. "This one here was obviously special. I settled down pretty good, started breathing better. That first inning was pretty rough."
Price retired six straight before Jeter led off the fifth with his 11th homer, giving him 1,269 hits at the House that Ruth Built. The sellout crowd of 54,279 roared as the captain rounded the bases after his opposite-field drive to right, and cheered even louder when he came out of the dugout for a curtain call.
The fans continued to chant the shortstop's name as Giambi batted against Price, who struck out four and walked none.
Jeter had a chance to break the record in the seventh but grounded into a double play. He'll likely get another opportunity Monday night when New York opens a four-game series against the Chicago White Sox.
"They always say records are meant to be broken but this one, with the stadium closing here in a week, you know at least I know I tied for it," he said.
The Yankees, almost certain to miss the playoffs for the first time since 1993, are nine games behind wild card-leading Boston.
The Rays loaded the bases after Pavano departed, and Damaso Marte walked Akinori Iwamura to make it 7-4. Jason Bartlett followed with a sinking liner but Brett Gardner made a terrific tumbling catch to end the inning.
Gardner also made a diving catch to rob Gabe Gross of a hit in the eighth.
Jackson (11-11) never looked comfortable and dropped to 0-3 in his past three starts. He allowed New York's first three batters to reach before Rodriguez hit a 3-1 pitch into the bleachers in right-center for his 17th career grand slam.
"I got some balls up," Jackson said. "They took advantage of it. It just wasn't my day."
Rodriguez reached 100 RBIs for the 11th straight season with his 34th homer of the year. It also gave him at least 100 runs in 13 consecutive seasons.
Jeter reached on a perfectly placed bunt single and Giambi finished a 12-pitch at-bat with a walk to set up A-Rod's first grand slam since Sept. 25, 2007, at Tampa Bay.
RHP Matt Garza, who threw 83 pitches in Tampa Bay's 6-5 loss Saturday night, will start Wednesday's game against Boston on short rest. ... RHP Phil Hughes joined the Yankees on Sunday and will start Wednesday's game against the Chicago White Sox. ... Yankees 2B Robinson Cano was pulled before the fifth inning because Girardi was upset by his lack of hustle on a fielding play in the fourth. ... The Rays went 7-11 against the Yankees this year.