ST. PETERSBURG, Fla. >> The Tampa Bay Rays are still afloat in the AL division series.

Jose Lobaton hit a solo home run with two outs in the bottom of the ninth inning into the giant fish tank beyond center field, and Tampa Bay staved off elimination once again by beating the Boston Red Sox 5-4 Monday night.

Evan Longoria had a three-run homer and the Rays averted a playoff sweep, cutting Boston’s lead to 2-1 in the best-of-five series. Game 4 is Tuesday night at Tropicana Field, with Jake Peavy starting for the Red Sox against Jeremy Hellickson.

“Look at this whole week working up to today, and then this game is even more dramatic than the other games we had already won,” manager Joe Maddon said. “It’s really an incredible day for the Rays.”

Tampa Bay took a win-or-go-home game for the fourth time in nine days. The Rays did it with an unlikely stroke as Lobaton, who came off the bench to catch in the top of the ninth, connected against Red Sox closer Koji Uehara.

“It’s unbelievable. It’s something you can’t explain,” Lobaton said. “We never give up. We’re going to keep fighting.”

Back home after two weeks on the road, the Rays gave a sellout crowd of 33,675 little to cheer until Longoria homered on his 28th birthday. His three-run shot off Clay Buchholz with two outs in the fifth rallied Tampa Bay to a 3-all tie.

Pinch-hitter Delmon Young, who has a penchant for driving home key runs in October, put the Rays ahead 4-3 with an RBI grounder in the eighth.

The Red Sox tied it in the ninth after closer Fernando Rodney issued a leadoff walk to Will Middlebrooks. Dustin Pedroia’s RBI grounder made it 4-all.

With a runner on third, pinch-hitter Mike Carp was called out on strikes to end the inning. Carp batted for Quintin Berry, who entered as a pinch-runner for David Ortiz in the eighth.

Berry stole second on a close play that drew an argument from Maddon. But when Ortiz’s spot came up again in the ninth, Boston’s big slugger was out of the game.

Rodney got the win when Lobaton golfed a low pitch to right-center. The ball deflected off a fan trying to catch the souvenir and wound up in the 10,000-gallon tank where cownose rays swim around.

Maddon said he was studying his lineup card when he heard the crack of the bat.

“Look up and the ball is going towards the tank, which, nobody hits home runs there. Nobody does. How about that? It’s incredible,” he said.

Uehara did not allow a home run in his final 37 regular-season appearances. The last time he served one up was June 30 to Toronto slugger Jose Bautista.

“That was an exciting game. Well-played game,” Boston manager John Farrell said.

The Rays won three must-win road games in three cities over four days just to get into the division series, so they felt good about their chances of coming back against the Red Sox.

Especially with Alex Cobb on the mound. The right-hander beat Cleveland 4-0 in the AL wild-card game last Wednesday and has been one of the most consistent pitchers in the majors since August 2012.

The Red Sox were just as confident about the prospect of closing out the series.

“I’m sure there’s an attitude they have nothing to lose and just let it all hang out,” Farrell said. “That’s what we’ve been accustomed to for years against the Rays. As I mentioned before the series started, we have tremendous respect for them and we know it will be a very similar game tomorrow night.”

Buchholz, limited to 16 starts this season because of a neck strain that landed him on the disabled list for three months, beat the Rays twice this year while allowing no runs and five hits in 13 innings. He also entered his second career postseason appearance with a 2.26 ERA in nine career starts at Tropicana Field.

Cobb settled down after a shaky first inning in which he gave up a leadoff single to Jacoby Ellsbury, hit a batter with a pitch and walked Ortiz. But the Red Sox got only one run out of it, when second baseman Ben Zobrist made a throwing error while trying to turn a double play.

Cobb, celebrating his 26th birthday, retired eight in a row before walking Ortiz leading off the fourth. Mike Napoli followed with a single for the second hit off Cobb, yet Boston was unable to take advantage.

Ortiz tagged and went to third on Daniel Nava’s fly ball, then was nearly caught too far off the bag when Jarrod Saltalamacchia struck out and catcher Jose Molina threw to third base trying to pick off Ortiz. The inning ended with Stephen Drew hitting a grounder back to Cobb.

The Rays wasted opportunities against Buchholz, too.

James Loney doubled off the left-field wall to begin the second inning, but was erased when Desmond Jennings lined into a double play.

The Rays loaded the bases on two walks and Loney’s second hit of the night, but Buchholz escaped the jam by fanning Matt Joyce.

Buchholz wasn’t as fortunate in the fifth, when Yunel Escobar beat out an infield single and David DeJesus doubled with one out. Zobrist popped to shortstop, bringing up Longoria, who became the second player in major league history to hit a postseason homer on his birthday.

Willie Mays Aikens homered twice for Kansas City on his birthday Oct. 14, 1980, against Philadelphia in Game 1 of the World Series.

Longoria’s home run was his ninth in 109 career postseason at-bats.

Loney had three hits off Buchholz, who allowed three runs, seven hits and struck out five in six innings.

Ellsbury scored Boston’s first two runs, on Zobrist’s throwing error in the first and Cobb’s wild pitch in the fifth. Ortiz’s fifth-inning RBI single put the Red Sox up 3-0 against the Tampa Bay starter.

NOTES: Rays rookie Wil Myers left before the eighth inning because of cramping in both legs. A leading contender for AL Rookie of the Year, Myers took an awkward swing on a foul ball in the seventh and grabbed the area around his left calf. He limped back to the dugout after striking out for the third out. Myers went to right field after the inning, then headed back to the infield and was met by a team trainer. The club said he received IV fluids, and Maddon said Myers probably will be fine for Tuesday night’s game. Joyce, the DH, replaced Myers in right field.