Matt Joyce homered, doubled and scored three runs for the Rays. Ben Zobrist and Carlos Pena each added RBI singles in the seventh, and Tampa Bay handed Miami its fourth straight loss.
"We've got to do better than that if we want to compete," Marlins manager Ozzie Guillen said. "That's the bottom line. I won't say we're not hitting. We've had good at-bats and put ourselves in situations to get something going. When we get on the bases, we don't do the job we should."
Ricky Nolasco (6-4) battled in six innings, giving up three runs while striking out six. The right-hander posted a season-high four walks, but he kept his team in the game.
"We're just struggling right now. It's going to happen," Nolasco said. "Hopefully we come back tomorrow and turn it around. We've swung the bats really well. We'll be fine. Tomorrow, I wouldn't be surprised if we put up a big number of runs."
But the Marlins were unable to cash in on numerous opportunities in the series opener.
Rays right-hander Jeremy Hellickson pitched out of trouble throughout his 4 1/3-inning outing. He walked seven and gave up five hits. But the Marlins were only able to touch him for one run. Burke Badenhop, the former Marlin, induced a big double-play grounder off the bat of John Buck in the fifth inning. Badenhop was credited with the win.
"It wasn't an oil painting," Rays manager Joe Maddon said. "Hellickson had real good stuff, but the command just wasn't there. Badenhop was the star of the game for us."
While the Rays got some breathing room late, Guillen noted the Marlins had let the game slip away in the first six innings.
"The kid who started the game for them, he can't even finish [the fifth inning]," Guillen said. "He was walking people. We have people all over the bases. We couldn't take advantage. If we want to compete, we've got to do better in that department."
Joyce's home run to right to open the fifth inning gave the Rays a two-run cushion, and they never looked back.
After the Marlins' fourth straight loss, all on the homestand, they are now three games behind the Nationals in the National League East. During the slide, Miami has totaled just four runs.
Situational hitting, once again, was a struggle, and the Marlins were 0-for-8 with runners in scoring position.
What transpired on Friday closely mirrored their performance on Thursday. The Marlins left 11 on base and went 0-for-13 with runners in scoring position in an 8-2 loss to Atlanta.
In Interleague Play, the Marlins are now 2-2. They took two of three at Cleveland, May 18-20.
Tampa Bay rebounded from allowing the tying run in the third to reclaim a 2-1 lead in the fourth inning. Again, the Marlins was tagged for a two-out RBI hit. Jose Lobaton doubled to open the inning, and he moved to third on Hellickson's one-out sacrifice bunt.
Will Rhymes was credited with an RBI single on a hard grounder that Omar Infante made a terrific play to reach. Infante dove and snared the ball, but his throw from the ground pulled Greg Dobbs off first base, allowing the go-ahead run to score.
Miami had pulled even at 1 in the third inning on Dobbs' sacrifice fly to center.
The Marlins loaded the bases with no outs after Infante's double and walks to Hanley Ramirez and Giancarlo Stanton.
Miami was only able to push across one run, and for the third straight inning, the club stranded two baserunners.
Missed chances hurt because Tampa Bay struck for a run in the third. Nolasco collected two quick outs, but the inning was prolonged on Joyce's bloop double to left. Austin Kearns, reinstated on Thursday night after being on the disabled list with a right hamstring strain, was unable to catch up with the ball near the left-field foul line.
B.J. Upton slapped an RBI single to left, giving the Rays a 1-0 lead.
With a struggling offense, any runs allowed are problematic.
The Marlins' sixth, seventh and eighth hitters -- Kearns, Chris Coghlan and Buck -- combined to go 1-for-11 with a walk.
"The only thing I don't see is us running across the plate," Guillen said. "That's all I can say. I can't be Joe Genius on what to do and what not to do. Whatever they're doing, do the opposite. Whatever they're doing right now is not working. We have to do better than that, especially the bottom of the lineup. They've got to dig in and try to help the guys on top."