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ST. PETERSBURG, Fla. -- A two-run homer and a nice defensive play more than soothed Curtis Granderson's aching body Wednesday night.

The Yankees center fielder made up for a fielding gaffe that led to a loss the previous night, backing a solid pitching performance by Freddy Garcia to lead New York to a 4-0 victory over the Tampa Bay Rays.

Granderson lost a ball in the Tropicana Field roof for a hit that paved the way for Tampa Bay to rally for a 3-2 victory Tuesday night.

He homered off David Price (9-8) in the first inning on Wednesday, then made a running catch on a ball hit by Evan Longoria to preserve a two-run lead for Garcia in the fifth.

"Initially when it was hit, I thought right away I might have had a shot," Granderson said. "I didn't know how hard it was hit, how far it was hit. The main thing was continue to get back there and see what happens. I saw that one all the way."

Garcia (8-7) scattered eight hits, struck out seven and walked none over 6 2/3 innings. The right-hander worked out of tight spots with runners in scoring position four times and reliever Boone Logan bailed him out of another by striking out Casey Kotchman in the seventh.

David Robertson pitched a 1-2-3 eighth for the Yankees, and Mariano Rivera added a perfect ninth in a non-save situation to finish the combined shutout.

Price, who is 20-6 all-time against AL East opponents, allowed two runs and six hits in 7 1/3 innings. He walked two, struck out five and hit Granderson in the back with his final pitch of the game.

"Ouch," Yankees manager Joe Girardi said. "It started off great with the two-run homer and then he hit a ball off his calf, and then he got drilled in the back. ... He is a little beat-up."

The second-place Yankees won for the fourth time in five games, remaining 1 1/2 games behind Boston in the AL East. Third-place Tampa Bay has lost six of eight to fall a season-high eight games off the pace in the division.

The Rays have been shut out in three of their past seven games and 10 times overall -- nine since June 1.

"These shutouts are really tough to watch sometimes," Rays manager Joe Maddon said after his team slipped to 23-25 at home, compared to 28-20 on the road.

"Again, it's similar to the beginning of the season when we had that very difficult start. We're just not swinging the bats well in this ballpark. It's so difficult to understand. We had opportunities with the right hitters at the plate. That also makes it more difficult."

Price allowed a home run to Granderson for the second time this season and a left-handed batter for only the fourth time in his career. Boston's Jacoby Ellsbury went deep against the 25-year-old lefty last week and Philadelphia's Chase Utley homered off Price in 2009.

Derek Jeter singled leading off the game, collecting career hit No. 3,009 -- one shy of tying Hall of Famer Wade Boggs for 25th on the all-time list -- off the same pitcher who yielded his 3,000th on July 9 at Yankee Stadium. Granderson followed with his 26th homer to give Garcia all the support he would need.

The Rays are 2-4 during a critical seven-game homestand against Boston and New York, the teams they are chasing in the division.

"It's very frustrating," Price said. "Obviously this team wants to win, and more importantly be playing in October. We've got to pick it up and start winning some games."

The Rays stranded runners in scoring position in four of the first five innings, including the fifth when Johnny Damon singled and advanced to third on Kotchman's third hit -- a two-out double. Longoria followed with the long drive to center that Granderson retreated to catch just before crashing into the wall.

"(Longoria) thought it came off the bat hot. It looked to me like it was carrying really well," Maddon said. "But again, the wrong part of the ballpark. ... He hit it well, but you've got to hit it better than well to get it out there."

Garcia struck out Matt Joyce, Longoria and Sean Rodriguez to get out of jams in the first, third and fourth.

Eduardo Nunez's two-run single off Cesar Ramos gave the Yankees a 4-0 lead in the ninth.

Game notes

Girardi hasn't ruled out moving LF Brett Gardner into the leadoff spot and dropping Jeter into the two-hole against right-handed starters with 3B Alex Rodriguez out of the lineup after having surgery on his right knee. Rodriguez is working out in a pool as part of his rehab program. ... Price has allowed a home run in four consecutive starts for the first time in his career. ... Rays RF Ben Zobrist was not in the starting lineup after fouling a pitch off his right calf on Tuesday night. ... New York IF Eric Chavez (broken left foot) went 4-for-5 as the DH in his second game with Class A Tampa. He will play defense on Thursday. RHP Rafael Soriano (right elbow inflammation) is scheduled for his second rehab appearance in Thursday's game. Both could rejoin the Yankees next week. ... Girardi said RHP Ivan Nova, who hurt his right ankle in a start at Triple-A Scranton/Wilkes-Barre on Tuesday, was feeling better, although he'll miss his next scheduled start after being placed on the 7-day DL.