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.
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.
In Minneapolis, Jake Peavy pitched eight crisp innings to win for the first time in more than six weeks, and Chicago swept a three-game series in Minnesota for the first time in more than seven years.
Brent Lillibridge, Paul Konerko , Alexei Ramirez and Alex Rios homered for the White Sox, who had lost 29 of 36 games to Minnesota until winning three straight at Target Field this weekend. The backsliding Twins have lost seven of their last eight games overall.
Peavy (5-5) last picked up a victory by pitching four shutout innings in his first career relief appearance, June 25 against the Washington Nationals, three days after he beat the crosstown rival Cubs with a so-so start.
In Arlington, Texas, Elvis Andrus hit a go-ahead two-run single in Texas’ five-run eighth.
Josh Tomlin shut out the Rangers over seven innings, but the 25-year-old right-hander walked Mike Napoli leading off the eighth and gave up a single to Mitch Moreland , his final batter.
Sidearm right-hander Joe Smith (2-3) came in, giving up an infield single to Yorvit Torrealba to load the bases.
In Kansas City, Missouri, Johnny Giavotella hit his first major league home run and doubled, leading Kansas City to the victory.
Giavotella, promoted Friday after hitting .338 in 110 games with Triple-A Omaha, is 5 for 11 in his first three games.
Giavotella led off a three-run fourth with a double and hit a solo home run in the fifth.
Bruce Chen (6-5) left in the sixth after a 46-minute rain delay. He gave up three runs and five hits, striking out five without a walk.
Chen allowed three hits to start a three-run sixth.
In Baltimore, Ricky Romero pitched eight innings of four-hit ball and Brett Lawrie hit his first major league homer.
John McDonald had three hits and two RBIs for the Blue Jays, who took two of three from the Orioles and have won seven of 11 overall.
Romero (10-9) struck out five and walked none to win his third straight start, a streak that began on July 27 with a victory over Baltimore. The only runs the left-hander allowed were on solo homers by Mark Reynolds .
In St. Petersburg, Florida, Josh Willingham led off the 10th inning with a home run for Oakland.
Willingham lined a pitch from Jake McGee (0-1) into the left field stands for his 17th homer this season. Fautino De Los Santos (1-0) threw a scoreless ninth to pick up his first major league win and Andrew Bailey allowed two singles in the 10th before getting his 13th save.
In Anaheim, California, Ervin Santana pitched into the ninth inning of his fourth straight phenomenal start, and Mark Trumbo homered off Felix Hernandez .
Santana (8-8) held the Mariners to seven hits and won his duel with Hernandez (10-10), whose 12 strikeouts were one shy of his career high. Santana lost his shutout bid on Mike Carp’s one-out homer in the ninth, and manager Mike Scioscia pulled him two outs short of his third consecutive complete game.
