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Don Kelly and Delmon Young hit consecutive home runs in the first inning, then pitcher Doug Fister and the bullpen spent the rest of a thrilling game trying to preserve their lead.
They did — barely — with Jose Valverde striking out Alex Rodriguez to end it and set up an ALCS series against the Texas Rangers.
Before a new Yankee Stadium record crowd of 50,960, New York had its chances, but the hosts went 2 for 9 with runners in scoring position and 0 for 4 with the bases loaded, and they stranded 10 runners.
Despite leading the AL with 97 wins during the regular season, the Yankees' early exit in the first playoff round will set off a restless offseason search for more starting pitching and hitters.
Rodriguez was 0 for 4 with three strikeouts and hit just .118 in the series (2 for 18) while Mark Teixeira batted .167 (3 for 18). Robinson Cano, whose fifth-inning solo homer started the comeback attempt, was the Yankees' primary offense with nine RBIs.
Kelly and Young homered on the sixth and seventh pitches of the game from New York rookie pitcher Ivan Nova. They were the first back-to-back postseason homers in Tigers' history, and it was the third homer of the series for Young, who was acquired from Minnesota in August.
Young, the first Tigers player with three homers in a single postseason series, left in the seventh because of a mild left oblique strain and will be re-evaluated Friday.
Nova lasted just 31 pitches and six outs, and was replaced by Phil Hughes, beginning a procession from the Yankees bullpen to the mound.
Hughes was pulled after his 21st pitch, and replaced by Boone Logan, who lasted just seven pitches and two outs.
That was followed by the odd sight of C.C. Sabathia coming on as a reliever. All 421 of his previous professional appearances had been as a starter, and he threw 106 pitches three days previously in Game 3.
Detroit immediately tacked on a run for a 3-0 lead. Former Yankee Austin Jackson led off the fifth with a broken-bat double to left. After a pair of strikeouts, Cabrera was intentionally walked and Victor Martinez hit an RBI single.
New York had put increasing pressure on Fister, who kept escaping trouble as his pitch count ran up. He stranded one New York runner in the second, two in the third then three in the fourth.
Cano's solo homer in the fifth cut the deficit to 3-1, then in the seventh, the Yankees loaded the bases with one out for the second time. Tigers reliever Joaquin Benoit walked Mark Teixeira to make it 3-2, the struck out Nick Swisher to end the inning.
In the bottom of the eighth, Brett Gardner singled with two outs and Derek Jeter momentarily lifted Yankees hopes with a big hit to right field, but it was caught on the warning track.
Valverde pitched the ninth for his second save of the series, remaining perfect in 51 chances this year.
Detroit won its first all-or-nothing postseason game since beating St. Louis in Game 7 of the 1968 World Series.
With the Tigers vying for their first World Series title since 1984, ace Justin Verlander will start the ALCS opener at Texas on Saturday night against the Rangers' C.J. Wilson.