David Price worked into the eighth inning, and Tampa Bay benefited from a controversial call to nip Boston, 2-1, in the makeup of a rainout from last Thursday.
Price (6-5) earned the fifth win in his last six starts by scattering two hits, including a Brandon Snyder solo homer. He also had eight strikeouts over 7 1/3 innings. Fernando Rodney picked up his 26th save with a scoreless ninth.
Sean Rodriguez hit an RBI double and Wil Myers knocked in the other run for the Rays, who vaulted over their Monday foes into first place in the AL East by a half-game.
"To Toronto and then here and New York and then back here against some really good pitching, to come out 8-2, I would absolutely take that," said Rays manager Joe Maddon.
Felix Doubront (7-5) allowed eight hits and two runs over five full frames for the Red Sox, who couldn't push the tying run across in the bottom of the eighth.
Price came back out after a 39-minute rain delay, and fanned Jonny Gomes looking for the first out in the frame, then was replaced by Joel Peralta. Ryan Lavarnway doubled off the Green Monster, then Stephen Drew hit a long single off the base of the low wall in right but pinch-runner Daniel Nava held up. Snyder then lifted a fly to left, and it appeared Nava beat the throw home with his foot across the plate, but was called out to end the inning.
Red Sox manager John Farrell was ejected by home-plate umpire Jerry Meals for arguing the call.
"It's unfortunate. We should still be playing now," Farrell said in the postgame.
In the ninth, Jacoby Ellsbury stroked a leadoff single and stole second after Shane Victorino popped out. Dustin Pedroia grounded to short, then David Ortiz was given a free pass and both runners moved up on a wild pitch, but Mike Napoli fanned to end the contest.
Tampa picked up a run in the fourth. Yunel Escobar singled with one out and a two-out Jose Molina hit moved him to third ahead of a Rodriguez double that allowed him to cross the plate.
It was 2-0 for the visitors in the fifth as Evan Longoria led off with a ground-rule double to center, moved up on a Ben Zobrist hit and scored when Myers was safe at first on a potential double-play grounder.
Price motored along, allowing one hit through five innings, until Snyder's slicing drive clanged off the Pesky Pole in right with one down in the home sixth.
Victorino robbed Luke Scott of a potential two-run homer with a catch against the bullpen wall in the seventh. Myers had drawn a leadoff walk against Jose De La Torre before Drake Britton served up what ended up being a long out.
With his Monday victory, Price became the first starter to beat the Red Sox twice at Fenway in a five-day span since Rip Collins of the St. Louis Browns did it on May 14 and 17, 1931 ... Longoria extended his hit streak to 11 games ... Tampa has won 22 of its last 26 games since June 29... Doubront has posted 14 consecutive starts allowing three or fewer earned runs, matching Pedro Martinez (2002) for the longest streak by a Sox pitcher since 1996 ... Despite the setback, Boston has won 10 of its 16 matchups with the Rays this season ... Prior to the contest, the Rays acquired pitcher Jesse Crain from the White Sox in exchange for players to be named or cash considerations ... Also on Monday, it was revealed that former Red Sox and Brewers slugger George Scott passed away at the age of 69. A moment of silence was observed in his honor.