John Jaso drove in two runs with a bases-loaded single that made it 5-5 and chased Matsuzaka in the sixth. Bartlett's sacrifice fly off Ramon Ramirez (0-2) drove in pinch-runner B.J. Upton after Matt Joyce and Sean Rodriguez singled to open the Tampa Bay seventh.
Randy Choate (2-2) struck out the only batter he faced – bailing the Rays out of a bases-loaded jam in the top of the seventh – to get the win.
Joaquin Benoit pitched a perfect eighth before Rafael Soriano got the final three outs for his 22nd save in 23 opportunities.
Eric Patterson, acquired last month to provide depth for an injury-depleted Red Sox roster, hit a pair of solo home runs off Tampa Bay starter Matt Garza. Kevin Youkilis, Adrian Beltre and Bill Hall drove in runs during a four-run third inning for Boston.
But the Rays bullpen held the Red Sox in check over the last five innings, giving an offense that's come alive over the past week an opportunity to get back into the game against Matsuzaka, who allowed five runs and eight hits in five-plus innings.
The Red Sox wasted an opportunity to break a 5-5 tie after loading the bases with one out in the seventh on Patterson's third hit and two walks. Balfour struck out Beltre, then Choate came on to fan J.D. Drew to end the threat.
Garza, who beat Matsuzaka and the Red Sox 9-5 at Fenway Park last week, allowed four runs and seven hits while throwing 84 pitches over three innings.
Six consecutive Red Sox reached base after the Rays starter retired the first two batters in the third, with Patterson starting a four-run uprising with his first homer since being acquired last month after All-Star Dustin Pedroia went on the 15-day disabled list with a broken left foot.
David Ortiz walked and scored on a triple by Youkilis. RBI singles by Beltre and Hall put the Red Sox up 4-1.
Patterson homered again off Andy Sonnanstine with two outs in the fourth, giving Matsuzaka a four-run cushion that the right-hander couldn't hold.
Evan Longoria's fifth-inning sacrifice fly trimmed Tampa Bay's deficit to 5-2. The Rays added another run in the inning when a passed ball, charged to Kevin Cash, permitted Carl Crawford to score from third base.
Crawford had three of Tampa Bay's eight hits off Matsuzaka, including a RBI double in the first inning.
Notes
Boston All-Star RHP Clay Buchholz (10-4, 2.45 ERA) was placed on the 15-day disabled list because of a strained left hamstring. Lefty Felix Doubront was recalled from Triple-A Pawtucket to start Tuesday night against the Rays. Buchholz could return to the rotation shortly after the All-Star break. … Tampa Bay's B.J. Upton, who's 1-for-13 lifetime against Matsuzaka, did not start. He entered the game as a pinch runner in the seventh, scored the go-ahead run and remained on defense in the eighth. … Boston RHP Josh Beckett, on the DL with a lower back strain, is scheduled to pitch in a rookie-level Gulf Coast League game Tuesday in nearby Sarasota. If the GLC game is postponed by rain, Beckett will throw a simulated game at Tropicana Field against Red Sox minor leaguers.