Moore looked right on track for another subpar performance from the outset when he found trouble in the first. After surrendering a leadoff single to Mike Aviles and striking out Dustin Pedroia, David Ortiz singled before Moore hit Adrian Gonzalez to load the bases.
Moore appeared up to the challenge, striking out Will Middlebrooks for the second out before getting ahead 0-2 to Cody Ross. The veteran then proceeded to work the count to 3-2 before drawing a free pass to put the Red Sox up 1-0.
Moore struck out Daniel Nava to end the threat, but the damage had been done in the form of a 33-pitch inning.
Marlon Byrd led off the second with his first home run of the season and Ross added a solo blast with two outs in the third to put the Red Sox up 3-0.
"I just had to flush," Moore said. "You can't control what just happened, so there really was no sense in me thinking too much. I just really tried to get it out of my mind as fast as possible."
Moore managed to gut out six innings, looking more like the pitcher who finished the 2011 season in the fashion that created all the hype surrounding him. He retired the last 10 batters he faced, giving him his first quality start since April 20 against the Twins.
Moore threw 68 pitches in his first three innings and just 38 over his final three, allowing three runs on five hits while walking one and striking out eight, moving to 1-4 on the season after taking the loss.
"After the second or third inning, [the ball] started coming out a little bit easier," Moore said. "I don't know if I was just letting my leg go down nice and easy or what, but it did feel like my arm was coming through a little better."
Batterymate Chris Gimenez left with a favorable impression of Moore following the outing.
"Honestly, I know the numbers haven't really shown it," Gimenez said, "but he's been making steps in the right direction. It's just kind of up to him now to put it all together. Once he gets two or three quality starts together, I think it's really going to start rolling downhill for him and he's just going to kind of take it and run with it."
Moore hopes that Thursday night's performance can carry over into his next start.
"That's the plan," Moore said. "Obviously from a team standpoint this isn't a victory. But for myself and my individual performance, I was somewhat satisfied with the fourth, fifth and sixth innings."
Jeff Keppinger singled off Red Sox starter Felix Doubront in the third to drive home B.J. Upton with the Rays' first run, and Rich Thompson singled home Sean Rodriguez in the fourth -- with his first Major League hit -- to cut the Red Sox's lead to 3-2.
Any hopes of a comeback were dashed in the eighth, when Ross came through again, hitting a two-run single off Wade Davis to put the Red Sox up 5-2 and give him four RBIs on the night. Boston had runners in scoring position and an open base when Ross stepped to the plate, prompting a question to manager Joe Maddon about the wisdom of pitching to Ross with Nava on deck.
"I really liked Wade there a lot," Maddon said. "The other part is Nava has a really good eye, and if you're going to load the bases, where Wade's really going to have to come to him. This guy will work a walk, too. And it's a ground ball. I mean it's really a poorly hit ground ball. It's one of those things that worked for them and didn't work for us."
Boston manager Bobby Valentine rolled out five relievers to effectively cover the final 3 1/3 innings and earn the Red Sox their sixth win in their last seven games.
"I was just going after this game tonight," said Valentine about his bullpen management. "I felt the guys wanted this game; did everything we could to win it, not that I don't manage that way every day."