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ST. PETERSBURG, Fla. -- Evan Longoria has struggled at Tropicana Field this season. It took just one at-bat to make things seem much better.

Longoria hit a game-ending solo homer in the ninth inning to give the Tampa Bay Rays a 4-3 victory over the Cincinnati Reds on Tuesday night.

"That's just the type of player Longo is," said Rays pitcher David Price, who tied a career high with 12 strikeouts. "He's lethal, especially late in games. He wants to be at the plate at that time. I can guarantee you everybody in this clubhouse wants him up there, too."

Longoria sent an 0-1 pitch from Logan Ondrusek (3-3) into the left-field seats for his fifth homer in the last eight games. The previous four in this power stretch occurred on the road -- the All-Star third baseman has just three homers and four RBIs in 24 games at Tropicana Field in 2011.

"Going into the ninth, it was a pretty tough game for me offensively, again," said Longoria, who was hitless in his first three at-bats. "But to turn it around with one swing of the bat was a good feeling."

Johnny Damon homered and drove in three runs for the Rays, who have won nine of 11. Tampa Bay had never beaten Cincinnati before, losing the initial seven meetings.

Damon, with 2,653 hits, is one away from tying Ted Williams for 71st place on the career list.

"That's probably going to be the most special on the list," Damon said. "I think Ted Williams is top for me."

Damon played four seasons with the Red Sox, including the 2004 World Series championship team.

Jay Bruce connected in the top of the ninth for the Reds, tying it at 3 with a leadoff drive against Kyle Farnsworth (2-2). It was Bruce's 18th of the season and ended a drought of 84 at-bats without a homer.

"These are tough to take," manager Dusty Baker said of the difficult loss.

Cincinnati's Johnny Cueto gave up three runs and four hits in 7 2/3 innings. The right-hander had won his previous three starts, allowing two runs in 21 innings over the stretch.

Cueto retired 10 in a row before allowing consecutive one-out singles in the eighth to John Jaso and Sam Fuld. He retired Reid Brignac on a fly ball before Bill Bray entered and allowed Damon's bloop two-run double that landed just out of the reach of diving left fielder Chris Heisey and gave Tampa Bay a 3-2 advantage.

"That was a big hit by Johnny," Price said. "It was a clutch hit. He's got about 2,600 of them."

Heisey had the ball go in and out of the lights.

"It was so close," Baker said. "Very close. He had a beat on it."

The Reds had scored two runs in the top half of the inning to take the lead. Drew Stubbs got it started with a triple off Price, who took a perfect game into the fifth. Stubbs scored on Edgar Renteria's single, and Joey Votto added a tiebreaking RBI double with two down.

Price gave up two runs and six hits in 7 2/3 innings.

"Both of them were dealing," Baker said of Cueto and Price.

Damon got the first hit off Cueto, a leadoff homer in the fourth. Damon has gone deep nine times this season, one more than all of last season with Detroit in 145 games.

Price struck out four of his first five batters, with the final three -- Votto, Scott Rolen and Bruce -- all going down on fastballs that the scoreboard radar gun had at 97 mph.

Jonny Gomes became the Reds' first baserunner when his hard one-hop liner with two out in the fifth went off the glove of Brignac, who attemped a backhanded grab at shortstop. It was first ruled an error, then changed to a single later in the game.

Ramon Hernandez followed with a single to right that advanced Gomes to third. But Price struck out Stubbs to end the inning.

Brandon Phillips doubled and Votto walked with two out in the sixth, but Price got a grounder from Rolen on a 3-2 pitch.

Game notes

Phillips finished 1 for 4 on his 30th birthday. ... The Rays are planning to have RHP James Shields pitch on the Sunday before the All-Star break. ... Renteria has 899 career RBIs.