Meanwhile, the American League East-leading Yankees swept a doubleheader from the Blue Jays to increase their lead over the third-place Rays to 6 1/2 games.
The Orioles once again needed extra innings to beat the Mariners, but by doing so, they catapulted to the top of the AL Wild Card standings with an 85-64 record. Tampa Bay trails Oakland by 5 1/2 games for the second AL Wild Card spot.
The Rays still face steep odds as their magic number to be eliminated from the AL East race fell to eight games, while their magic number for elimination from the Wild Card race remained at nine.
Manager Joe Maddon said he knows that the odds are stacked against his team, so he would like his players to put on the blinders and not pay attention to the standings while trying to pile up the wins and hope for the best.
"We want to do a little bit of Minnesota Fats," Maddon said. "We have to involve Minnesota Fats, we've got to run the table, man."
Thursday's key games to watch (all times ET)
A's (Milone, 13-10) at Tigers (Sanchez, 8-12), 1:05 p.m. Preview >
Blue Jays (Laffey, 3-5) at Yankees (Hughes, 15-12), 7:05 p.m. Preview >
White Sox (Francisco Liriano, 6-11) at Royals (Guthrie, 4-3), 8:10 p.m. Preview >
Rangers (Darvish, 15-9) at Angels (Greinke, 14-5), 10:05 p.m. Preview >
If the postseason started today ...
This is how the teams would match up: Postseason Bracket »
To calculate a team's magic number, take the number of games it has remaining and add one. Then subtract the difference in the number of losses between that team and its closest pursuer.
A tiebreaker game will be played to determine a division winner, even if the tied clubs are assured of participating in the postseason. If a division championship tiebreaker is necessary, the head-to-head record between the clubs will determine home-field advantage. If the head-to-head record is tied, then the division record will be the next tiebreaker.
If two clubs are tied for the two Wild Card berths, home-field advantage will be determined by the head-to-head record between the clubs. If the head-to-head record is tied, then the division record will be the next tiebreaker.
2012 postseason schedule
Wild Card playoff games: Oct. 5
Division Series: Oct. 6-12
AL Championship Series: Oct. 13-21
NL Championship Series: Oct. 14-22
World Series: Oct. 24-Nov. 1
Bill Chastain is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.