After each team posted only one run through 13 frames, Atlanta's bats woke up when Chris Hatcher came on to pitch the top of the 14th. The usual big-inning recipe of walks, errors and timely hits helped the Braves notch a six-run frame.
Justin Upton delivered the game-winning hit, doubling home two runs to give Atlanta a 3-1 lead. The Braves followed with a pair of two-run singles.
"We were hoping to get multiple innings out of Hatcher there," Marlins manager Mike Redmond said. "Obviously, that didn't happen."
The loss marked Miami's first losing streak of four or more games since dropping nine straight from May 21 to May 30.
"We had tons of opportunities and just couldn't get the big hit," Redmond said. "In those games, those close games, it comes down to who's going to get it, and they got it.
"We've been on the other end of those games as well. It's tough. You battle and you fight and tonight, it just didn't happen."
Particularly disappointing for the Marlins was how the heart of the lineup -- Giancarlo Stanton, Marcell Ozuna and Logan Morrison -- fared with runners on base in the fourth, sixth, seventh and 13th innings.
After Ed Lucas reached scoring position with a one-out double in the fourth, Stanton walked, Ozuna flew out to right and Morrison grounded out to second.
Stanton led off the sixth with another walk, but Ozuna and Morrison followed with back-to-back flyouts.
Justin Ruggiano and Lucas drew consecutive one-out walks in the seventh, but Stanton struck out swinging and Ozuna grounded out to first to the end the threat.
The middle of the lineup finally showed some promise in the 13th, when Stanton led off with a single -- Miami's first hit since the sixth -- and Ozuna was hit by a pitch.
But Morrison put a dent in the threat by grounding into a double play. An Adeiny Hechavarria flyout stranded Stanton 90 feet from home.
"Those guys, they're going to go through some tough spells," Redmond said. "Everybody does. Those guys will be back out there again tomorrow and come back in those situations. ... I believe in those guys. I know they'll come through with the big hits. It just didn't happen tonight."
Hechavarria scored the Marlins' lone run in the fifth after leading off the frame with a single up the middle. The base hit extended the rookie's hitting streak to a season-high eight games. He finished 2-for-6 to record his 15th multihit game.
Braves starter Mike Minor retired the next two batters after Hechavarria before allowing back-to-back singles to pinch-hitter Placido Polanco and Ruggiano. Hechavarria scored on Ruggiano's hit.
Polanco's base hit proved key, but it came at a cost. Slowey was done after five innings.
"My spot came up," Slowey said. "We obviously scored that run and the hope is that we can make that last."
Slowey exited the game after giving up only four hits in five scoreless innings. With Miami trying to decide how to address Nolasco's vacated rotation slot in the second half, Slowey made a strong case to rejoin the rotation on Monday night.
"I was thankful for the results," Slowey said. "I wish I could've gone longer. Obviously, in a game like that, you want to go wring out every last pitch you have."
"It was tough because he's making the start, and he hasn't thrown more than two innings in a month. He gives us five solid innings, and he was done. It was time to move on," said Redmond.
Once Minor exited the game after 6 1/3 innings, the bullpens battled.
Miami's bullpen was solid through the 13th inning, giving up only one run and retiring 24 Atlanta batters in a row.
"You look at the job the bullpen did," Slowey said. "They did a wonderful job. They really did a great job of giving us opportunities to put the game away."
Redmond added: "The bullpen guys did a great job. I was happy with the way we pitched."
The Braves' bullpen countered, giving up only two hits in 7 1/3 scoreless frames and retiring 15 Marlins in a row between the eighth and the 12th.
"Their guys threw great, too," Slowey said. "They're a great pitching staff, great bullpen. They have been all year. Any run that we get is tough to come by, especially against those guys."
The Marlins had several opportunities to earn their third straight victory against the NL East-leading Braves, but repeatedly came up short. In the midst of a season-best run, Miami wants to do more than simply come close.
"You want to win these games," Slowey said. "You want to win games [in which] you feel like you have a great team kind of on the ropes. It's tough not to win."