It was their first win in Boston in six tries this season.
"We have to beat these guys," manager Joe Maddon said. "You have to beat the people in front of you in the division, obviously. We've done a pretty good job over the years; this year has been awkward.
"Hopefully this is the kind of game that can push you in the right direction."
The first Major League RBIs for Myers came at a good time. Entering the seventh inning with a 3-2 lead, Evan Longoria plated a run with a single to left field off reliever Craig Breslow. James Loney followed with a double, and Myers stepped up with two outs and two runners in scoring position.
Myers quickly fell behind 0-2 against Alex Wilson, looking at a fastball over the plate and swinging out of his shoes on a slider off the plate. He then roped a fastball to right field, sprinted around first and pulled up at second for his first career extra-base hit.
"That hit by Wil is a big hit," Maddon said. "Those add-on runs are significant in this ballpark, because they can come back at any moment.
"He ran better than I had been told. He threw better than I had been told. He's a good defender. He's an athlete, is what he is. And as he gets more comfortable out there, he's going to be a fine outfielder. He's the proverbial five-tool guy, maybe six tools with the makeup. You can see the power there. He's on the right path."
Myers finished 1-for-4, and is 2-for-11 through his first three Major League games, but his two-run double put the Red Sox away.
"The seventh inning was probably the pivotal point," said Boston manager John Farrell. "We were in a one-run ballgame, and particularly the RBI 0-2 base-hit to Myers, that gave them enough of a spread to keep us in check."
Hellickson looked much better after allowing eight runs in one inning against the Royals his last time out. He needed just 88 pitches to get through six innings, walking none and allowing two runs while striking out four. He pitched quickly and efficiently, only getting hurt by a pair of infield hits by Jonny Gomes that drove in both Boston runs.
"I'm right where I want to be," said Hellickson, who hasn't walked a batter in four games as he lowered his ERA to 5.50 on the season. "Like I've been saying, I'm just trying to eliminate that big inning I've been giving up. Tonight, it was good to see."
Offensively, the meat of Tampa Bay's lineup came through, as the No. 2 through No. 6 spots combined to go 10-for-23 with five runs and six RBIs, including a solo homer from Desmond Jennings in the first inning. Ben Zobrist and Longoria followed with singles, and Loney launched a sacrifice fly to right field to drive in another.
Jose Molina scored in the bottom of the fifth, capping off a 3-for-4 night, just the third time in two years he's posted a three-hit game. The 6-foot, 250-pound catcher hustled from second base to score, and Maddon joked "the vortex almost pulled me into his jet stream."
Molina slid in safely under the throw from Jacoby Ellsbury.
"I think I did one of those Matrix kind of moves," said the catcher, not the fastest of runners.
Maddon was happy to see his players in a good mood before they head to New York, where they'll begin a four-game set with the Yankees on Thursday.
The Rays are keeping their heads above water in the American League East with a 37-35 record.
"Mentally, as we walk into Yankee Stadium tomorrow, it can only help," Maddon said. "I like the fact that nobody was in any kind of panic mode. Everybody came in today focused, ready to play. That was a tough day yesterday. That was tough for the Red Sox too, but they won two. So that was nice that we were able to come back, put that in the rearview mirror and play as well as we played."