Swisher's run-scoring single triggered a three-run second inning and Curtis Granderson socked his 33rd homer -- the 200th of his career -- in the sixth as the Yanks took the rubber match of a three-game series.
Starter Freddy Garcia lasted only 4 2/3 innings, allowing a pair of runs, but Boone Logan (5-2) took over and provided 1 2/3 scoreless frames to earn the victory.
Indians starter Ubaldo Jimenez (9-13) absorbed the loss, yielding three runs on eight hits in a five-inning effort.
Carlos Santana supplied a two-run single for the Tribe.
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