Boston has been shut out 11 times this season, and twice in the last four games.
"Consistency, yeah, that's been elusive," said manager John Farrell. "Tonight, I felt we did another very good job of creating opportunities, particularly in the fourth and sixth innings. In the sixth inning, we've got a first-and-third situation and they're able to make a couple of key pitches, get a couple of strikeouts and a groundout to end the threat. The ability to string base hits together has been inconsistent."
David Ortiz thought he had put the Sox on the board with one swing in the top of the first, when he lined one to right. But a fan reached over and caught the ball before it could clear the fence on its own.
First-base umpire Vic Carapazza ruled it fan interference, and that call stood after a crew chief review.
Ortiz was still miffed about it after the game.
"That was a homer. That was a home run," Ortiz said. "I don't care what they say. That was a homer. They [messed] up on that one right there. But I watched the whole replay -- that was a home run. They say the guy reached over. The guy, he reached over, but the pressure of the ball pulled him down. That ball was going to be over the yellow line over there."
Veteran starter Jake Peavy was traded to the Giants before the game, and Boston's players realize that more moves could be on the horizon as the clock ticks to Thursday's non-waiver Trade Deadline.
John Lackey turned in a solid performance, giving up eight hits and three runs (two earned) over seven innings.
"Yeah, it's a weird day when you lose a buddy, for sure," Lackey said of Peavy's departure. "Talked to him at the hotel when he was about to leave. He's going to a great situation, a guy he's played for before, a division he knows really well. Wish him all the luck. Mostly I'm going to miss my buddy more than anything."
There was more frustration for the Red Sox in the bottom of the first.
Desmond Jennings opened by tapping a bunt in front of the plate, and Red Sox catcher Christian Vazquez snagged it and made an errant throw to first. Jennings moved all the way to third. The Red Sox thought there might have been interference by Jennings running down the first-base line.
"The explanation I got was that he didn't interfere with the throw," said Farrell. "Well, there was no deflection, but that 45-foot line is there to protect the first baseman, and [Mike Napoli] had to alter his course to receive the ball. Nonetheless, [home-plate umpire] Chad [Fairchild] felt there was no interference."
After a walk to Ben Zobrist, Matt Joyce laced an RBI single to right to give the Rays a 1-0 lead.
"You don't want to be in the stretch the third pitch of the game for sure, but things happen. Managed the inning, gave up one run and gave the guys a chance," said Lackey.
In the fourth, Vazquez thought he helped the Red Sox snuff out a possible rally when he made a strong throw to second in an attempt to pick off Yunel Escobar.
But Escobar was ruled safe, and Farrell opted not to challenge.
"When we reviewed it internally, it wasn't conclusive," said Farrell. "Where we were at that time of the game, given our history with when we've used the system before, when it's not conclusive, we're not going to risk using the one challenge we have at that moment."
Tampa Bay then made it a 2-0 game on an RBI single to left-center by Kevin Kiermaier, driving home Escobar.
Lackey understood Farrell's predicament, but still wished there was a challenge.
"Yeah, a challenge would have been nice there," said Lackey. "Looked like he was pretty out. But you're right, sometimes they still don't overturn when it looks pretty [conclusive], so you never know. We've had it go both ways this year so, what are you going to do?"
In the sixth, after a quirky single by Jonny Gomes fooled Evan Longoria, Boston had first and third with nobody out. But Stephen Drew and Xander Bogaerts both struck out, and Jackie Bradley Jr. grounded out.
Lackey was solid for the most part. Zobrist belted a two-out solo shot to right in the seventh to make it 3-0.
The Rays have won nine in a row to inch back into contention, something the Red Sox, who are 10 1/2 games back of first-place Baltimore in the American League East and 7 1/2 behind in the Wild Card standings, wish they could do.
"It's really impressive," said Rays manager Joe Maddon. "We've just been playing good baseball."