New York trailed 3-1 in the ninth, but scored twice off Rays closer Fernando Rodney, who blew his fifth save of the season. Brennan Boesch and Brett Gardner delivered back-to-back, two-out RBI hits to force extra frames.
Ivan Nova (2-1) wiggled out of a bases-loaded, one-out jam in the bottom of the 10th to extend the game and Overbay decided it with a two-out solo blast in the 11th off Josh Lueke (0-2).
Mariano Rivera tossed a 1-2-3 bottom of the 11th for his 18th save in as many opportunities as the Yankees clinched their three-game series.
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