ARLINGTON, Texas — Buck Showalter and the Baltimore Orioles will get another chance to overtake the New York Yankees.

The surprising O’s have already beaten some big odds, getting past the two-time defending AL champion Texas Rangers and their Japanese ace, Yu Darvish, in the win-or-go-home wild-card playoff.

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Joe Saunders pitched effectively into the sixth inning at a place where he had never won, Adam Jones delivered the tiebreaking sacrifice fly and the Orioles, in the playoffs for the first time in 15 years, eliminated the Rangers, 5-1, Friday night.

‘‘With our team it’s just a bunch of guys that raised the bar and wouldn’t give in and still haven't. Now they get a chance to win, to roll the dice, and there’s a lot of good card players in there,’’ said Showalter, their manager.

The Orioles advanced to play the East champion Yankees, the AL’s top seed — the teams split 18 games this season. The best-of-five division series starts Sunday at Camden Yards.

The upstart Orioles spent the whole second half chasing New York, never passing the Yankees and falling just short in a neck-and-neck race for the division title.

Turns out, the Yankees haven’t brushed off these Birds just yet.

‘‘Real proud of everybody. Tacking on runs were big, knew they were going to run at you,’’ Showalter said. ‘‘But just a real proud moment for us.’’

After twice coming with a strike of winning last year’s World Series, this season is over that quickly for the Rangers, who were in first place for a majors-high 178 days this season. Texas loaded the bases with two outs in the ninth before David Murphy flied out to end it.

‘‘We just didn’t get it done,’’ manager Ron Washington said.

The Rangers lost the AL West crown on the final day of the regular season, after being swept in three games at Oakland for a stretch of nine losses their last 13 games.

‘‘I'm not stunned, I was right there watching it,’’ Washington said.

Their worst slump of the season came at the wrong time for Texas, which a week ago had a four-game division lead with six games to play. Because of that, they couldn’t avoid the majors’ new winner-take-all postseason openers, and then couldn’t get past the Orioles with their top pitcher on the mound.

‘‘To be honest with you I never thought anything like this would happen,’’ Washington said.

Wiped out by San Francisco in the 2010 World Series, the Rangers twice came within a strike of their first World Series championship last October against St. Louis.

‘‘Me and my teammates and the Rangers’ fans, I don’t think we all thought that it would end this early,’’ Darvish said through a translator. ‘‘I mean, right now, no. I don’t even know what I'm supposed to do tomorrow.’’

Saunders quickly gave up the Orioles’ 1-0 lead in the first, but that was the only run he allowed in 5 innings. The lefthander struck out four and walked one.

Even though it was the postseason, the Orioles stuck to the regular Friday night uniforms — including black tops and caps with script O’s instead of the traditional cartoon bird.

With the new format, it was a postseason game after an extra day.

The new rules also eliminated the prohibition against teams from the same division meeting in the ALDS, setting up the Orioles and Yankees.

For the Rangers, they’re headed into their longest offseason in three years.