Trailing 3-1 in the seventh inning, Chris Nelson led off with a single against Yoervis Medina and went to second on a wild pitch.
One out later, Charlie Furbush (0-2) relieved, issued a walk to Brett Gardner and then grooved a pitch to Cano, who blasted it off the base of the right-center field fence for a two-run double.
Lyle Overbay followed by lofting a sacrifice fly for the decisive run.
Shawn Kelley (2-0) earned the win and Mariano Rivera racked up his MLB-best 16th save as the Yankees notched their sixth win in seven games.
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