Wil Myers finished with two hits and two RBI, and David Price went the distance, as Tampa topped Boston, 5-1, in the third edition of a four-game series from Fenway Park.
Price (5-5) scattered five hits and a Mike Napoli homer, needing only 97 pitches to finish his third complete game of the season.
James Loney, Luke Scott and Jose Molina drove in a run each for the Rays, who closed the gap in the AL East to a half-game once more thanks to their 17th win in 20 July contests.
"We're playing good baseball. Regardless of what it says on the other jersey, we're playing well," Rays manager Joe Maddon said.
Felix Doubront (7-4) worked 6 2/3 innings, allowing six hits and three runs for the Red Sox, who have dropped five of their last seven.
Napoli cleared the seats above the Green Monster with one out in the seventh to pull the Sox within 3-1, but the Rays countered with two more in the eighth on back-to-back RBI singles from Loney and Molina.
Price then set down the final eight Boston batters in turn to complete his outing.
"He threw some pitches we could have hit, but we just didn't do it," Red Sox catcher Jarrod Saltalamacchia said.
Tampa broke through in the third, after loading the bases with one out on two singles, an error and a sacrifice.
Myers dumped a two-run hit to center, then stole second while Ben Zobrist stole third, and the latter came in on a Scott sacrifice fly.
Myers has collected at least two hits in each of his last six games ... Prior to the contest, the Sox made it official with second baseman Dustin Pedroia, signing him to an eight-year contract beginning in 2014 and continuing through the 2021 season. The deal is reportedly worth $110 million. Pedroia had been signed for 2014 at $10 million under his old deal.