With the win, the Red Sox took over sole possession of first place in the AL East and clinched a win in the
season series against New York for the first time since 2004.
The Yankees led 2-1 on homers by Eduardo Nunez and Brett Gardner before Mariano Rivera came in to close it out in the ninth.
But Marco Scutaro led off with a double for his fourth hit of the game. He moved up on a sacrifice and scored on a sacrifice fly to send the game into extra innings.
It was the fifth blown save of the season for Rivera, who pitched a scoreless inning in each of his first two appearances against Boston this season.
"That's huge. He's the best closer in the game right now," Reddick said.
David Ortiz sparked the game-ending rally with a one-out double against Phil Hughes (2-4). Darnell McDonald came in to run and the Yankees opted to walk Carl Crawford, who had three hits.
Reddick then hit a liner into the corner in left, driving in McDonald as the Fenway Park crowd erupted in cheers.
Daniel Bard (2-5) pitched a scoreless 10th for the win.
Boston lost the series opener but won the next two to snap the Yankees' eight-game winning streak and take the series. The Red Sox are 10-2 against New York this season with six games left, and one game up in the AL East.
Gardner had three hits for the Yankees, including the tiebreaking drive with two out in the seventh. He also stole two bases, giving him 35 on the season.
Nunez tied it with his homer in the fifth — one batter after Russell Martin was thrown out by Reddick trying to stretch a single into a double.
Meanwhile, the Red Sox kept producing baserunners -- and stranding them. They left the bases loaded in the second and sixth, and stranded a pair in the fourth.