Rays pinch-hitter Sean Rodriguez connected for a tiebreaking, three-run homer in the seventh. Yunel Escobar hit a two-run double later in the inning and then took third on defensive indifference, setting off the fracas.
Escobar, Rodriguez and Boston's Jonny Gomes were all ejected.
This is Boston's longest losing streak since an 11-game skid from June 8-19, 1994. The Red Sox have been outscored 52-24 over their last 10 games.
Boston will try to end the drought on Monday afternoon in a game at Atlanta.
Xander Bogaerts hit a two-run single with two outs in the Boston ninth off Josh Lueke. Grant Balfour got his ninth save by retiring Dustin Pedroia on a grounder.
Gomes pulled Boston even at 3 with two-run, pinch-hit homer in the seventh off Joel Peralta (2-3). It was Gomes' eighth pinch-hit home run.
After Craig Breslow (2-1) walked pinch-hitter Desmond Jennings and gave up Evan Longoria's single to start the seventh, Rodriguez gave the Rays a 6-3 advantage with his first pinch-hit homer.
Escobar doubled and easily took third without a throw on the first pitch to Jose Molina.
Escobar got into a yelling match with the Boston dugout and had to be restrained just before both benches and bullpens emptied. The sides gathered around third base for a short session that mostly involved pushing and shoving.
Longoria hit a leadoff homer and Logan Forsythe had an RBI single as the Rays took a 2-1 lead in the fourth. Longoria's opposite-field drive to right off Brandon Workman was his first since May 6.
Wil Myers made it 3-1 on a run-scoring grounder in the fifth.
Workman, recalled from Triple-A Pawtucket before the game to replace injured left-hander Felix Doubront (strained left shoulder), gave up three runs and five hits over five innings in his first big league start this season. He made three relief appearances with Boston earlier this year before being optioned to Pawtucket on April 8.
Rays starter Jake Odorizzi allowed one run and four hits in six innings. The Red Sox went 0 for 7 with runners in scoring position against the right-hander.
Boston had runners on second and third with no outs in the third, but scored just once for a 1-0 lead on a sacrifice fly by Brock Holt.
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