The Rays had some cause for concern when Matt Moore was hit in the face on a comebacker by Xander Bogaerts and left the game after four innings.
Moore seemed to deflect some of the force of the liner with his glove, but the Rays took the necessary precautions and the lefty exited the field on a golf cart. In the clubhouse, Moore received stitches for a laceration on his lip. The club reported that no concussion symptoms were detected and a hospital trip would not be required.
"I thought it hit his glove," Bogaerts said. "He got up and he threw me out. I definitely didn't think it got him in his face. It wasn't my intention, obviously. I wish him nothing but the best. Hopefully he'll have a good recovery."
Over four innings, Moore held the Red Sox hitless while walking four and striking out four.
Matt Joyce ripped a three-run homer for the Rays on the last pitch that Doubront threw.
"The whole team really came out swinging today," said Joyce, who made his return to the lineup from a short layoff with neck stiffness. "That's always fun to be part of something like that and it helps everyone feel more relaxed up at the plate."
The Rays also got a solid contributions David DeJesus and Desmond Jennings, who both had two hits and two RBIs.
After being no-hit for the first six innings, the Red Sox got their bats in gear in the seventh.
After one out, Jonny Gomes got on base with a walk and Bogaerts followed by lacing Boston's first hit of the day, a single to left-center. Will Middlebrooks smashed an RBI single in the inning.
Up next: Lefty Drake Britton draws the start for Monday's 1:05 p.m. ET game at Sarasota, Fla., against the Orioles (watch on MLB.TV). Righty Jake Peavy will stay in Fort Myers and pitch in a Minor League game. Lefty Craig Breslow will do the same in his first game action of 2014. Andrew Miller and Francisco Cordero will pitch in relief of Britton against the Orioles.