The phone from the dugout to the bullpen malfunctioned in the seventh inning, but the Rays soon got their signals straight, and four pitchers combined on a seven-hitter to beat Miami 4-2.
In the three-game series, the Rays outscored their intrastate rivals 22-7.
"We got really good pitching," manager Joe Maddon said. "The bullpen has been spectacular."
The biggest problem in the finale was getting a reliever ready. With James Shields nursing a two-run lead and the phone not working, Maddon called time so reserve infielder Will Rhymes could trot out to the bullpen with instructions regarding who should warm up.
"Rhymesy looked like the fastest," Maddon said with a smile. "The pitchers (in the dugout) are so disinterested at that point. They've been eating food the whole game, so they're not really able to run down to the bullpen. Rhymesy was eager. He had that look in his eye, so I felt good about it."
The phone problem amused Marlins manager Ozzie Guillen.
"Ozzie was playing with Joe, acting like he had yanked the cord out," Rays shortstop Elliot Johnson said. "We had to call a 30-second timeout."
The Rays earned their fifth sweep this season and won their seventh game in a row against the Marlins. Miami fell to 0-6 on its homestand and has been outscored 43-10.
"We've got to play better," Guillen said. "We really were pretty flat at the plate all weekend."
Johnson hit his third home run and Matt Joyce hit his 11th to help the Rays (35-25) improve the best record in the American League. Shields (7-4), who had lost his past three decisions, allowed one run in 6 1/3 innings to win for the first time in his past five starts.
"I'm definitely pleased," Shields said. "I felt pretty good for the most part. Overall it was a good start -- better than the last few."
Anibal Sanchez (3-5), plagued again by lousy run support, pitched six innings and allowed four runs, including both homers. He has made 12 starts this season, and the Marlins have scored 18 runs with him in the game.
Sanchez lost for the fifth time in his past six outings.
"The team is really down with the situation the way it is right now," he said. "We're not scoring too much, and we're leaving too many on."
Gaby Sanchez, recalled before the game after a three-week demotion to Triple-A, doubled in the seventh to drive in the Marlins' first run. Teammate Logan Morrison, back in the lineup after being benched for two games because of a slump, had three hits and drove in a run.
But the Marlins went 2 for 11 with runners in scoring position. They're 5 for 50 in those situations during the homestand.
The Rays have won four games in a row and went 4-2 on their trip after scoring just one run in the first two games against the Yankees.
"It's a little bit of a roller coaster," Joyce said. "That's the way hitting goes. There are ups and downs. Hopefully we keep it going."
"Up and down the lineup, it's just getting better," Maddon said.
Morrison doubled with one out in the second inning, but Shields put out that threat and retired 10 in a row until pinch hitter Justin Ruggiano doubled to start the sixth.
Shields pitched out of that jam, too, striking out Giancarlo Stanton to end the inning.
Upton doubled off the scoreboard to drive in a run for Tampa Bay in the first inning.
Joyce led off the fourth inning with a homer into the first row of the center-field seats. Zobrist singled, and with one out Johnson homered for a 4-0 lead.
RF Stanton slid headfirst on the warning track after he made a leaping catch to rob Zobrist of a hit. ... The crowd of 31,111 included 648 tickets for dogs on bark at the park day. ... The Rays began the day with the best record in the AL at 34-25 (.576). That's the lowest winning percentage by the league leader on June 10 since 1959. ... Josh Beckett, the Marlins' World Series star in 2003, pitches against them for the first time Monday when Miami opens a series against the Boston Red Sox at home. ... The Marlins' ERA is 3.08 on the road and 4.72 in their new ballpark.