They got some help in their quest to accomplish that goal from the Red Sox Monday night, who took a 4-3 victory over the arch-rival Yankees thanks to Jacoby Ellsbury's walk-off single in the ninth inning.
The Yankees and Orioles are tied for both the East and the No. 2 Wild Card spot. Meanwhile, the A's appear poised to take a firm grasp of the top Wild Card after a dramatic win over the Angels Tuesday night.
Leading by a run, the A's scored twice in the top of the ninth, before allowing the Angels to do the same in the bottom of the frame, while putting men on first and third with no outs. Reliever Jerry Blevins promptly recorded a strikeout and a double play to secure a 6-5 victory.
In the National League, the story has become all about the Wild Card race, as all three division leaders have built leads of six games or more.
But it's becoming quite a showdown for that Wild Card as struggles by the teams on top have allowed for the Brewers (four back), Phillies (four back) and D-backs (five back) to creep back into the chase.
The three teams they're chasing -- the Cardinals, Dodgers and Pirates -- all lost Tuesday.
"I know because of the distance we have, and all the teams ahead of us, that for me it's just not worth really watching that too closely," Brewers manager Ron Roenicke said of the Wild Card race. "I'd rather just watch how we're playing."
In the AL Central, the Tigers drew to within two games of the division-leading White Sox with a 5-3 victory on Tuesday. They could draw even by the end of the series with their top two pitchers, Max Scherzer and Justin Verlander, slated to throw the final two games.
Today's key games to watch (all times ET)
Marlins (Johnson, 8-11) at Phillies (Lee, 4-7), 4:05 p.m. Preview >
Suddenly very alive in the NL Wild Card hunt, the Phillies send left-hander Cliff Lee to the mound against the Marlins at Citizens Bank Park.
Cardinals (Lohse, 14-2) at Padres (Richard, 12-12), 6:35 p.m. Preview >
Almost by default, the Cardinals remain in possession of the second Wild Card spot. They hope to avoid a sweep at the hands of the Padres.
Rays (Cobb, 9-8) at Orioles (M. Gonzalez, 6-4), 7:05 p.m. Preview >
Again, the O's find themselves tied with the Yankees atop the AL East, but the Rays are lurking just two games back for the division and No. 2 Wild Card.
Yankees (Phelps, 3-4) at Red Sox (Cook, 3-9), 7:10 p.m. Preview>
The Red Sox may be out of the hunt, but they could spoil the Yankees' season as a consolation prize. New York is tied with Baltimore for the division lead.
Pirates (Burnett, 15-6) at Reds (Bailey, 10-9), 7:10 p.m. Preview >
Losers of five straight, the Bucs have gotten help from just about everyone -- except themselves. They're still in the NL Wild Card hunt, just 2 1/2 games behind St. Louis.
Braves (Maholm, 12-9) at Brewers (Gallardo, 14-8), 8:10 p.m. Preview >
Sitting just four games out of the playoffs, the Brewers are very much alive as they go for a sweep of the Braves, who hold the top Wild Card spot.
Tigers (Scherzer, 15-6) at White Sox (Floyd, 9-9), 8:10 p.m. Preview >
The Tigers could cut into their two game deficit in the NL Central with a victory over the division-leading White Sox, who send Gavin Floyd to the hill.
Giants (Lincecum, 8-14) at Rockies (Francis, 5-4), 8:40 p.m. Preview >
The Giants appear poised to pull away in the NL West, as their lead over the second-place Dodgers has grown to six games.
Dodgers (Harang, 9-8) at D-backs (Cahill, 10-11), 9:40 p.m. Preview >
Aaron Harang gets the ball for the slumping Dodgers, who, despite their 6-10 record since adding Adrian Gonzalez and Josh Beckett, remain one back of the No. 2 Wild Card spot.
A's (Griffin, 5-0) at Angels (Santana, 8-11), 10:05 p.m. Preview >
In the third game of a four-game set, the A's look to grab a firm hold of the top Wild Card spot, while the Angels look to crawl back into the hunt.
If the postseason started today ...
Wild Card: Orioles or Yankees at A's
Division Series: Orioles or Yankees vs. White Sox | Rangers vs. Wild Card winner
Wild Card: Cardinals at Braves
Division Series: Reds vs. Giants | Nationals vs. Wild Card winner
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 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 division record will be the next tiebreaker.
Tiebreaker rules »
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