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ARLINGTON, Texas -- Closer Joe Nathan got the quick redemption he hoped for, and the two-time defending AL champion Texas Rangers are back in the playoffs.

They're still trying to win another division title.

Nathan ended a long day with his 37th save, after blowing a chance in the opener, and Mike Napoli homered twice while driving in six runs as the Rangers won 8-7 Sunday night for a doubleheader split against the Los Angeles Angels.

"Any reliever would ask to get out there and try and put this afternoon's game behind them," Nathan said. "The team over there is playing great, pushed us right the limit again. We've still got some work to do."

While overcoming a quick 4-0 deficit in the nightcap to assure themselves a playoff spot -- and postseason berths for Baltimore and New York, as well -- the Rangers (93-66) have to win at least once during their season-ending, three-game series at second-place Oakland for the AL West title.

"You would think there would be a letdown, but because these guys take each game for what it is, there is no letdown," manager Ron Washington said. "Yes, it was a tough loss the first one. ... Fell down 4-0, it was no big deal. They went out there and put some good at-bats together and they played with a lot of energy and Joe got a chance to redeem himself."

While the Rangers wrapped up a spot in the playoffs, they did see third baseman Adrian Beltre exit in the seventh inning after reaggravating a left shoulder strain. Beltre left right after leaping with his left arm fully extended above him in an attempt catch Angels first baseman Mark Trumbo's liner. Beltre got his glove on the ball, knocking it down. When he put his arm down, he let the glove fall to the ground and took a few steps.

Washington quickly came out of the dugout with a trainer to check on Beltre. After a brief discussion, rookie Mike Olt took over at third base.

The Rangers said Beltre initially strained his shoulder diving for a ball in the first game Sunday.

"Hopefully it's nothing serious, and I'll be back out there tomorrow," Beltre said. "I knew it was pretty sore, but I couldn't afford to sit. I didn't say anything to anybody. I tried to get through it but Wash didn't let me finish."

Los Angeles (88-71), which won the opener 5-4 on Torii Hunter's two-run double with two outs in the ninth off Nathan, trails the A's by three games for the AL's second wild card with three games left.

The Angels have to sweep their three-game series in Seattle and have Texas do the same against Oakland to force a tiebreaking 163rd game between the A's and Angels for the second wild card.

"These guys played their hearts out," manager Mike Scioscia said. "I don't know that you can ask much more than that."

After only his third blown save for Texas in the opener, Nathan worked through the heart of the Angels lineup in the nightcap.

Los Angeles led 4-0 after only five batters off Derek Holland (12-6) in the second game, but Ervin Santana (9-13) quickly squandered after his former teammate went deep on him twice.

David Murphy and Napoli hit back-to-back homers in the second as Texas closed to 4-3. Josh Hamilton had a double in the first for his 127th RBI.

Napoli's 23rd homer an inning later made it 6-4 and chased Santana, who has given up a majors-high 39 homers. Napoli drove a two-run double into the left-center gap in the fifth to make it 8-4.

It was Napoli's 10th career multihomer game, four of them against his former team the past two seasons. Napoli played five years for the Angels before being traded twice in five days before the 2011 season, to Toronto and then Texas.

"Sometimes there's going to be that hitter you don't match up well against," Scioscia said.

Mike Trout, who in the opener became the first major league rookie to reach 30 homers and 40 stolen bases in the same season, struck out to start the second game against Holland.

But the Angels then had four straight hits. Albert Pujols had an RBI double and scored on a single by Hunter before Trumbo's 32nd homer, a two-run shot.

Nathan took over after Koji Uehara struck out the side in the eighth. Uehara has retired all 23 batters faced his last nine games, with 15 strikeouts.

Holland managed to get into the seventh inning, and didn't allow any more runs until a three-run homer by Howie Kendrick, the last batter he faced. The left-hander, who made it only three innings his previous start, struck out five while allowing seven runs and 12 hits.

Hunter, who lives in nearby Prosper, had seven hits in the doubleheader. He is hitting .350 (98 of 280) since the All-Star break, and his game-winning double into the left-center gap came right after Nathan (3-5), his former teammate in Minnesota, struck out Trout.

The Angels are still trying to make up for two bad slumps. After adding slugger Pujols and left-hander C.J. Wilson this winter, they were 8-15 in April. They had a 4-13 slide to start August.

But they still have a chance to make the playoffs after winning 11 of their last 16 games, if they get a lot of help from the Rangers.

So what do the Angels do now?

"We go to Seattle and fight like hell," Trumbo said.

Game notes

Garrett Richards (4-3) retired Nelson Cruz with two runners on in the eighth in the opener, and Ernesto Frieri pitched a perfect ninth in the opener for his 24th save in 26 chances. ... Yu Darvish struck out seven in 6 2/3 innings in the opener, when Cruz hit his 24th homer and also threw Trout out on the bases from right field. ... Texas ended with a regular-season attendance of 3.46 million, an average of 42,720 per game -- both franchise records. ... Holland and Santana was the scheduled matchup for Saturday's game, which was called off four hours after its scheduled start because of rain. ... The 21-year-old Trout is the youngest player with a 30-30 season. He needs two stolen bases to become only the third player ever with 30 homers and 50 stolen bases. The others? Eric Davis (1987) and Barry Bonds (1990).

Information from ESPN Dallas.com's Richard Durrett and The Associated Press was used in this report.