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.
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.
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.
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.
NOTES: Boston put 1B Mike Napoli on the 15-day disabled list with a sprained finger on his left hand. ... Rays RHP Jeremy Hellickson (arthroscopic right elbow surgery) threw batting practice for the second and is set to pitch in an simulated game Wednesday. He expects to return before the All-Star break. ... Tampa Bay 2B Ben Zobrist (dislocated left thumb) hit against Hellickson and hopes to come off the disabled list next weekend. ... Boston manager John Farrell said Ortiz will play first base in at least once in the two-game interleague series against the Braves.