ST. PETERSBURG, Fla. -- A lot of the Yankees were probably fast asleep early Wednesday morning when another piece of their playoff puzzle fell into place.

They've known for a while that the Oakland Athletics will be their opponent in the American League Wild Card Game and it became official at 2:07 a.m. EST Wednesday.

The Athletics still were mathematically alive in the AL West until they lost their Tuesday night game in Seattle 10-8 in 11 innings on a two-run, walk-off homer by Chris Herrmann.

The Athletics' loss clinched the AL West for the Houston Astros, who had lowered their magic number to one with a 6-2 home win earlier Tuesday night over the Los Angeles Angels.

The Yankees and Athletics will play a win-or-go-home Wild Card Game on Wednesday, Oct. 3. The game probably will be played at Yankee Stadium, as the Yankees now hold a 2 1/2-game lead over Oakland plus the tie-breaker.

The Yanks can clinch home field for the Wild Card on Wednesday with a win in Tampa Bay plus another Oakland loss to the Mariners.

The Yanks and Athletics split their six games this season with each club winning two of three at home.

Yankees manager Aaron Boone has been impressed with Oakland, a small-market club that wasn't expected to contend this season.

"When we played them at our place in May, we recognized some of the young talented players that were emerging for them," Boone said before the Yankees' 9-2 win in Tampa Bay on Tuesday night. "They certainly had a lot of guys really blossom.

"Through trades and stuff, they've really added to what was already a very good bullpen. They're a really good team, we understand that, and I think all of baseball and all of the American League, especially as the second half has unfolded, has seen just how dangerous they are."

Randy Miller may be reached at rmiller@njadvancemedia.com. Follow him on Twitter @RandyJMiller. Find NJ.com on Facebook.