David Price threw 8.2 innings in his Tigers' debut and Alex Avila hit a game-winning home run in the top of the 12th as Detroit beat the Yankees, 4-3, on Tuesday night at Yankee Stadium.

Alex Avila homered in the 12th inning to give the Tigers the win (Getty Images).

The loss drops the Yankees to 58-54 and puts them one full game back of the Blue Jays in the chase for the second wild card. The Yankees are tied with the Mariners at 1.0 back and both teams trail the Royals, who are just 0.5 back.

The Tigers struck first on Tuesday, scoring in the top of the first inning when Victor Martinez hit a sacrifice fly that scored Rajai Davis, who had led off with a single.

Brian McCann erased that lead with a homer in the bottom of the second and the Yanks took a 2-1 lead in the third on a double by Jacoby Ellsbury. The Pinstripes added to it with a solo homer by newly-acquired Martin Prado in the fifth.

That was all Price would yield, and the Tigers came back to tie the game via solo runs in the sixth in the seventh, the latter which came on a single from Avila.

The game remained tied until Avila struck again in the 12th, lifting a home run off Matt Daley.

Hiroki Kuroda threw seven innings and allowed three runs in a no-decision Tuesday (Getty Images).

Price allowed the three Yankee runs in his debut, also surrendering eight hits and walking none while striking out 10. Hiroki Kuroda worked seven innings for New York, also allowing three runs.

The two teams will play again tonight at 7:05 p.m. Chris Capuano will pitch for the Yankees against struggling Tigers ace Justin Verlander.