Burger, who went 3-for-4, hit his homer off reliever Kirby Yates (7-2).
Miami's Jazz Chisholm Jr., who had three steals, belted a grand slam later in the eighth inning. He is approaching a potential 20-20 season, with 17 homers and 22 steals.
Marlins reliever Tanner Scott (8-4) earned the win, getting the final four outs.
There were eight homers hit in the game — four by each team.
For the Braves, Matt Olson set the single-season franchise record for home runs, hitting No. 52. That's one more than Andruw Jones hit in 2005.
Ozzie Albies hit his 30th of the season, tying his career high. Austin Riley slugged his 36th homer and Michael Harris II hit his 18th, which is one shy of what he had as a rookie last season.
Besides Burger and Chisholm, Miami was also led by Yuli Gurriel, who slugged a three-run homer, and Luis Arraez, who went 3-for-5 with a solo blast. Arraez leads the majors with a .351 batting average.
Atlanta opened the scoring in the first as Albies hit a two-run homer and Riley followed with a solo dinger.
Miami took a 4-3 lead in the bottom of the first as Arraez hit a leadoff homer, and Gurriel followed with his three-run shot.
The Marlins extended their advantage to 5-3 in the third as Burger doubled and scored on Garrett Hampson's two-out single. Burger beat a strong no-hop throw from right fielder Kevin Pillar.
Harris' homer in the fifth cut Atlanta's deficit to 5-4, and Olson tied it 5-5 with his shot in the sixth.
In the eighth, Josh Bell drew a two-out walk, and Burger followed with his 411-foot homer to right-center. Chisholm put the game away with Miami's first grand slam of the season.
—Field Level Media