David Ortiz's three-run homer saw the Red Sox edge to a 3-2 win over the Rays at Tropicana Field.
It was Boston's first win in six games and halted the Rays' winning streak at nine.
Rays pitcher Chris Archer was unhappy with Ortiz, whose bat-flip celebration angered him.
"He feels like he's bigger than the game," he said.
"He feels like the show is all about him when in reality, if I don't walk Daniel Nava, if I don't give up an infield single to [Dustin] Pedroia, his home run means nothing."
The Toronto Blue Jays' Yankee Stadium hoodoo is well and truly over as a 5-4 win in New York gave them a series victory a day after they ended a 17-game losing streak at the ground.
Manny Machado's one-out sac fly in the 10th saw the Baltimore Orioles edge the Seattle Mariners 3-2.
Carlos Santana homered twice as the Cleveland Indians crushed the Kansas City Royals 10-3 and Josh Harrison had four hits in the Pittsburgh Pirates' 7-5 victory over the Colorado Rockies.
The Cincinnati Reds' struggles continued as they were beaten 4-2 by the Washington Nationals, while the Miami Marlins beat the Houston Astros by the same score.
The Philadelphia Phillies overcame the Arizona Diamondbacks 4-2 and the Minnesota Twins avoided being swept by the Chicago White Sox, winning 4-3.
David Freese's homer in the eighth saw the Los Angeles Angels past the Detroit Tigers 2-1 and the Atlanta Braves were 8-3 winners against the San Diego Padres.
A five-run second inning set up the Oakland Athletics' 9-3 win over the Texas Rangers and the Los Angeles Dodgers completed a sweep of the San Francisco Giants with a 4-3 victory.
The New York Mets claimed a 2-0 win over the Milwaukee Brewers and Matt Holliday's first-inning homer guided the St Louis Cardinals past the Chicago Cubs 1-0.