The Rays beat the Baltimore Orioles 7-4 as Matt Joyce collected three RBIs, and their three-game winning streak has put them ahead of the Red Sox.
Boston led the San Francisco Giants 2-1 but allowed their opponents to level in the eighth, and the in the ninth former Red Sox man Marco Scutaro drew a walk with the bases loaded to finish things off.
Tampa Bay continue to lead the wild-card race in the American League from Boston and then the Oakland Athletics, who were beaten 7-4 by the Seattle Mariners.
Oakland trail the Texas Rangers .579 to .568 in the AL West after Adrian Beltre's two-run blast led the Rangers to a 4-2 victory over the Houston Astros.
The AL Central-leading Detroit Tigers suffered a 6-3 loss at the hands of the Minnesota Twins as Justin Morneau was a triple shy of a cycle, collecting four RBIs.
A two-run homer from Drew Stubbs in the 14th inning inspired the Cleveland Indians to a 4-1 win over the Los Angeles Angels.
A one-out single by Lonnie Chisenhall propelled the Indians in the same inning before Stubbs' first homer since July 4 sealed a victory.
The New York Yankees won both ends of a double-header against the Toronto Blue Jays to make it eight wins out of 10.
The first contest saw three-run homers from Robinson Cano and Chris Stewart power the Yankees to an 8-4 success as Ichiro Suzuki moved to within one hit of 4,000 in his career, while Jayson Nix was the hero of their 3-2 win in the nightcap.
Nix tied the game with a home run in the seventh inning and then won it with a walk-off single in the ninth.
John Danks tossed eight scoreless innings and Gordon Beckham homered as the Chicago White Sox beat the Kansas City Royals 2-0.
In the National League, Yasiel Puig came off the bench to hit the go-ahead homer in the eighth inning as the Los Angeles Dodgers topped the Miami Marlins 6-4. Puig had been benched and fined after reporting late for the game.
The win keeps the Dodgers 7.5 games clear of the Arizona Diamondbacks, who beat the Cincinnati Reds 5-2 behind a grand slam from Paul Goldschmidt, a shot which moved him to 100 RBIs for the season.
The Diamondbacks now trail Cincinnati by five in the wild-card standings.
Pittsburgh strengthened their hold in the NL Central with an 8-1 win over the San Diego Padres, while the Pirates' rivals, the St Louis Cardinals, fell 6-3 to the Milwaukee Brewers as Sean Halton drove in three runs.
The Atlanta Braves were beaten 5-3 by the New York Mets while the Washington Nationals topped the Chicago Cubs 4-2.
Troy Tulowitzki's 22nd home run of the year led the Colorado Rockies to a 5-3 victory over the Philadelphia Phillies.