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ARLINGTON, Texas -- Evan Longoria is still limping. Now he's also hitting, and the Tampa Bay Rays are headed home, one victory from an improbable comeback.

Longoria snapped out of his postseason slump with a homer and two doubles, Carlos Pena scored twice with a pair of extra-base hits of his own and Tampa Bay escaped elimination again with a 5-2 victory Sunday over the Texas Rangers to force a deciding Game 5 in the AL Division Series.

"We've really battled to get back to even," Longoria said. "And I think we have a lot of confidence going home, and being able to finish the series in our home ballpark."

To do that they'll have to beat Cliff Lee who matched a postseason best with 10 strikeouts in a 5-1 series-opening victory. The Rays lost the two games at Tropicana Field before winning twice in Texas to push a division series to a fifth game for the first time since the Los Angeles Angels beat the New York Yankees in 2005.

"I still want to believe there is a home-field advantage and hopefully that's going to show up," manager Joe Maddon said. "The extra game at home, I have been talking about it all along."

If the Rays win they will join the 2001 Yankees as the only teams to lose the first two games at home and still win a five-game series.

The series winner hosts Game 1 of the AL Championship Series Friday night against the Yankees. New York swept Minnesota in three games, clinching the other division series with a 6-1 win Saturday night.

Texas is still the only current major league franchise that has never won a postseason series, and still has not won a playoff game in front of its home fans (0-6).

"It's down to one game, we've got Cliff going and certainly feel good about that," Rangers manager Ron Washington said. "We have proved that we can win there."

Tampa Bay sends 19-game winner David Price to the mound Tuesday night in a rematch of the Game 1 starters.

"I like our chances with Dave on the mound again," Longoria said.

The Rays' resurgent offense helps, too.

Longoria, still limited by a left quad strain that forced him to miss the last 10 games of the regular season, was in an 0-for-12 slide before he and Pena had consecutive doubles starting the fourth against Tommy Hunter. Longoria added a two-run homer in the fifth for a 5-0 lead.

"I kind of felt like Kirk Gibson going around the bases," he said. "There are times when I have to try to push it. ... I know I hit the ball out of the ballpark, I'm not really going to run as fast as I can around the bases."

After hitting only .125 (8 for 64) with one run in the first two games, and going 16 innings without scoring in one stretch, the Rays were five outs from elimination before their bats finally came alive late in Game 3. And the positive trend carried over into Sunday, when they had 12 hits.

Tampa Bay has already gone from losing at least two in a row to winning at least three straight seven times this season, The Rays even pulled off that trick as part of a pivotal series against the Yankees just a few weeks ago.

Longoria's injury is obviously still bothering him when he runs the bases and on some plays at third base.

"He is under strict managerial orders to not run hard, although he can't anyway," Maddon said. "The ball's in the gap -- listen, the walking double, I'll take it every time. ... And, of course, the home run over the wall is a nice play."

Longoria got to jog around the bases after his first homer this postseason. He set a major league rookie record with six two years ago when the Rays won the AL pennant and went to the World Series.

Pena put Tampa Bay ahead to stay after he tripled off the base of the wall in left-center in the second. He scored when Matt Joyce hit a high popup in shallow right that dropped near backpedaling second baseman Ian Kinsler for an error.

Pena's .196 batting average in the regular season was the lowest among major league qualifiers, and his future in Tampa Bay is uncertain because he is a potential free agent. For now, Pena is hitting and making sure he and the Rays keep playing.

"I think all of us appreciate where we're at," Pena said. "It was extremely important for this team to turn the page."

In the final two innings of Game 3, Pena had an RBI single and a home run as the Rays wiped out a 2-1 deficit on way to a 6-3 victory.

Add in his first two at-bats Sunday and Pena hit for the cycle over a span of four at-bats.

Hunter struck out seven but allowed four extra-base hits in his four innings. He allowed three doubles while striking out the side in the fourth.

Rookie right-hander Wade Davis pitched into the sixth for the Rays, getting out of a base-loaded jam in the fifth when he struck out Vladimir Guerrero. Rafael Soriano worked a perfect ninth for the save.

When Davis walked Josh Hamilton to load the bases with two outs in the fifth -- with two relievers warming up -- Maddon and pitching coach Jim Hickey opted to leave the right-hander in the game.

Seconds later, Davis hopped off the mound with an emphatic fist pump and everybody in the Tampa Bay dugout responded in similar fashion.

"At that point in the game, for me, it was the game," Davis said.

Nelson Cruz hit the first pitch of the sixth for his third homer in four postseason games. Kinsler followed with a single and Davis, who struck out seven and walked three, was done.

Randy Choate retired the only batter he faced, Grant Balfour allowed an RBI double to rookie first baseman Mitch Moreland before getting out of the inning.

Before the series against Tampa Bay, the Rangers had played only the Yankees in the playoffs. Texas won its first-ever playoff game in 1996, but New York then won three straight that season and swept best-of-five series in 1998 and 1999.

Now they will be depending on Lee, acquired July 9 from Texas for these kind of situations, to earn a chance to play New York again in the postseason.

"It's been an unusual series so far," Kinsler said. "We won two games at their place and they won two games at ours. That's the way it stands and we hope it doesn't change."

Game notes

With his Game 1 victory, Lee is 5-0 in six career postseason starts. He went 4-0 with a 1.56 ERA in five starts for the Philadelphia Phillies in 2009, including 2-0 with a 2.81 ERA against the Yankees in the World Series. ... Hunter needed 12 pitches to get the first out of the game. Then Carl Crawford grounded into an inning-ending double play on the next pitch. Crawford grounded into only two double plays in 600 at-bats during the regular season. ... The game ended soon after the Dallas Cowboys kicked off their game at Cowboys Stadium, which is near Rangers Ballpark.