Ibanez's remarkable post-season continued when he hit the second of two two-run homers - Ichiro Suzuki crushed the first - as the Yankees incredibly erased a 4-0 deficit in the bottom of the ninth to force extra innings.
It made Ibanez the first man to hit three home runs in the ninth inning or later in the same post-season.
But this time it was not enough to earn the win for the Yankees as the Tigers built a two-run lead in the 12th through an RBI double from Delmon Young and a single from Andy Dirks, on which Yankees shortstop sustained an apparent ankle injury as he attempted to field.
And while Tigers closer Jose Valverde could not protect a four-run lead in the ninth, Drew Smyly, making his post-season debut, pitched his second scoreless inning in the 12th to register the win.
Earlier, Young had led the Tigers with a home run and an RBI single as the Tigers built a four-run lead before Valverde's ninth-inning blow-up.