Josh Hamilton dropped a fly ball in center field for a two-run error that put the A's (94-68) ahead 7-5 in a six-run fourth inning.
While Hamilton's Rangers (93-69) are headed to the new one-game, wild-card playoff, the A's get some time off before opening the division series in their first postseason appearance since 2006.
Both teams had to wait to learn their opponents from a pair of night games: Boston at New York, and Baltimore at Tampa Bay.
The A's would earn the AL's No. 1 seed if the Yankees lose, and open the division series at the winner of Friday's wild-card playoff featuring the Rangers. If New York wins, Oakland would be the No. 2 seed and begin at Detroit.
The A's needed a sweep and they delivered to win their first division crown in six years and 15th in all. They overcame a five-game deficit in the final nine days and took sole possession of the West's top spot for the first time this year.
"It shows how important Game 162 is," Oakland's Jonny Gomes said. "I don't think it took 162 to games to check the character of this ballclub."
Grant Balfour retired Michael Young on a fly to center for the final out, then raised his arms in the air as the A's streamed out of the dugout and began bouncing up and down in the infield.
"2012 AL WEST CHAMPIONS" flashed on the scoreboard.
Make it two champagne celebrations in three days for these A's. They clinched a playoff spot Monday and held a wild dance party in the clubhouse.
This time — in new gray AL West champion T-shirts — players took a victory lap through the rundown Coliseum, where the outfield still has a light patch of grass from football in the venue shared by the NFL's Raiders.
While the A's players circled the field, injured infielder Brandon Inge sprinted toward the right-field bleachers by himself, raised a gray T-shirt to the crowd then began dancing alone.
Soon, the celebratory champagne and beer made its way to the field — and players sprayed it into the stands.
Players came back onto the field almost an hour later to greet the fans still gathered along the top of the dugout.
Oakland pulled off another remarkable performance in a season defined by thrilling walkoffs, rallies and whipped-cream pie celebrations by a team that was never supposed to be here.
A club that trailed Texas by 13 games on June 30. A club with a $59.5 million payroll, lowest in baseball. General manager Billy Beane found ways to get a blue-collar franchise back to the playoffs for the first time since being swept by Detroit in the 2006 AL championship series.
"It was all part of the plan," Beane said before the game, planning to watch alone from the weight room in his usual routine. "It's a good day."
Coco Crisp hit a tying two-run double in the fourth against Derek Holland (12-7). Brandon Moss drove in three runs, including a two-run single in a four-run eighth.
Rookie Evan Scribner (2-0) left the mound to a standing ovation from the sellout crowd of 30,067 and wound up the winning pitcher. He allowed two hits and struck out two in three scoreless innings after replacing struggling starter A.J. Griffin.
Jerry Blevins relieved Scribner and struck out Hamilton to end the sixth before allowing a leadoff single to Adrian Beltre in the seventh. Ryan Cook, pitching for a fifth consecutive game, replaced Blevins and gave up a double to Nelson Cruz before retiring the next three Texas hitters with strikeouts of David Murphy and Mike Napoli. Catcher Derek Norris pumped his right arm as the Coliseum fans jumped to their feet.
Norris then homered leading off the bottom of the eighth for his second RBI. It was his seventh homer and Oakland's majors-leading 112th since the All-Star break.
"Ever since Day 1 I've been here, it's been, the A's can't compete with the payroll, can't compete with this team or that team," Norris said. "We're better off if we're down. It just gives us the extra energy. I hope they keep doing it."
The A's join the NL West champion San Francisco Giants as division champions. The Bay Area is already buzzing about a possible Bay Bridge World Series like the 1989 championship swept by Oakland, one interrupted by an earthquake.
Hamilton's miscue while charging forward might haunt the to-be free agent if his Rangers don't get past their wild-card game.
"I just missed it, man," Hamilton said. "If it moves, you can make adjustments if you break down. When you're running, you can't make the adjustments."
These are the same Rangers who twice came within one strike of the franchise's first World Series championship before losing Games 6 and 7 to the wild-card St. Louis Cardinals. It was Texas' second near miss in as many years after losing the 2010 World Series to the Giants.
Yoenis Cespedes punched his bat, apparently thinking he had recorded the last out before the ball glanced off Hamilton's glove. Manager Ron Washington stood with a stunned look in the dugout, then had an animated chat with Hamilton once the inning ended.
Murphy's two-run single highlighted a five-run third inning that put Texas in prime position.
Moss drew a leadoff walk from starter Ryan Dempster and Josh Reddick followed with an RBI double. Josh Donaldson singled and Seth Smith's base hit made it 5-3 and chased Dempster with none out and runners on first and second.
Washington turned to the lefty Holland, a starter who was tagged for four runs in the first inning of the second game of Sunday's doubleheader with the Angels before working into the seventh.
He retired the first two batters before Crisp's double down the right-field line. The A's batted around in the inning after Texas sent 10 to the plate in the third. And the A's kept adding on until the end.
The only other teams to come back from at least 13 games down to win the division were the 1914 Boston Braves, the 1951 New York Giants, the '78 Yankees and the '95 Seattle Mariners.
"Anything can happen in the long season," said Rangers pitcher Yu Darvish, who will start the wild-card game. "That's why we play 162 games. We're going to forget about this and get ready for the next one."
Oakland accomplished all this with an ever-changing roster managed by Bob Melvin in his first full season as A's skipper. They lost third baseman Scott Sizemore on the first full day of spring training workouts, never promoted slugger Manny Ramirez from the minors before parting ways, and dealt with devastating injuries all year long.
Opening day starter Brandon McCarthy took a line drive to the head Sept. 5 that required surgery and ended his season, Brett Anderson missed most of the year coming off Tommy John surgery, and Dallas Braden never pitched because of shoulder problems. Starter Bartolo Colon received a 50-game suspension in August for a positive testosterone test.
Third baseman Inge needed shoulder surgery last month and prized Cuban rookie Cespedes missed time with a pair of injuries in May and June.
And that's just the beginning for a team that traded away catcher Kurt Suzuki to the Nationals during the year after swapping three top pitchers during the offseason — Trevor Cahill to Arizona, NL Cy Young Award favorite and 21-game winner Gio Gonzalez to Washington and All-Star closer Andrew Bailey to Boston.
"There hasn't been a lot of luck involved," Beane said. "The one thing about baseball, when you play 161 games, you don't get lucky this late in the season. And, quite frankly, if you were to look into individual things and events that happened, starting with the first day of full workouts we lost our everyday third baseman. We had to figure out what we wanted to do. We haven't had a lot of good luck. There have been a lot of adjustments on the fly from that first full-squad workout when Sizemore went down."
The A's, whose 14 walkoff victories lead baseball, won their seventh game this year after trailing by four or more runs.
NOTES: The A's won the season series 11-8, just the second time in seven seasons they've done so. ... Texas' Geovany Soto snapped an 0-for-16 streak with a single in the third that chased Griffin. ... Texas also scored five runs in an inning vs. the A's Tuesday night winner Travis Blackley on Sept. 27. ... The sellout crowd included 1,000 standing-room only tickets. ... Holland pitched in relief for the second time this year.
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