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 allowing a run on four walks and striking out four.
Over 4 1/3 innings, Doubront gave up 10 hits and eight runs, all of them earned. Doubront walked two and struck out six while throwing 88 pitches.
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: The Rays travel to Fort Myers, Fla., for a second straight day Monday, this time to take on the Twins at Hammond Stadium. Chris Archer is scheduled to get the start for Tampa Bay, while the Twins will call on fellow right-hander Mike Pelfrey. First pitch is scheduled for 1:05 p.m. ET and can be seen live on MLB.TV.