Den Dekker led off the ninth with a single against Indians closer Chris Perez (5-3), went to second on Anthony Recker's sacrifice and broke the 1-1 tie when Young doubled to right field.
Asdrubal Cabrera got the only RBI for the Tribe, whose four-game winning streak was snapped.
The Indians came into the contest trailing Tampa Bay by 1 1/2 games in the chase for the final American League wild card spot.
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