Stanton hit a solo homer in the fourth inning and a two-run shot in the eighth.
With three games remaining, Stanton needs one more homer to join the 60-homer club, which includes only five players in the history of the game -- Babe Ruth, Roger Maris, Barry Bonds, Sammy Sosa and Mark McGwire.
Stanton has 129 RBIs, eight more than the previous franchise record set by Preston Wilson in 2000. Stanton has also scored 121 runs, which ranks third in the majors this year.
In Stanton's previous game, Wednesday afternoon at the Colorado Rockies, he went 0-for-3 with three strikeouts. However, he quickly got hot again in his first game after a six-game road trip.
Miami rookie Dillon Peters (1-2), pitching in Stanton's giant shadow, earned his first major league win, allowing just two hits and no runs in 5 2/3 innings. He walked four and struck out four.
In his previous 18 2/3 innings, Peters allowed 18 runs.
Braves starter Julio Teheran (11-13) took the loss. Despite entering the game with a career 5-2 record at Marlins Park and a 4-1 overall record in his past five decisions, Teheran was shaky, allowing eight hits, three walks and five runs in six innings.
Miami got to Teheran with four runs in the third inning. Dee Gordon started the uprising by pulling a triple into the right-center gap. He scored moments later when Teheran bounced a wild pitch past catcher Tyler Flowers.
The Marlins kept the rally going, loading the bases with two walks and an infield single. Justin Bour cashed in with a two-run single, and Derek Dietrich added a sacrifice fly.
After Stanton homered in the fourth inning, Atlanta's Lane Adams went deep in the seventh off Drew Steckenrider, cutting the Braves' deficit to 5-1.
Stanton's two-run shot in the eighth off Rex Brothers closed the scoring and was more than enough for Miami (75-84). Atlanta is 71-88.
NOTES: Marlins RF Giancarlo Stanton has hit 47 of his homers this year from the No. 2 position in the lineup, setting a major league record. Eddie Mathews hit 46 homers from the No. 2 spot in 1959. ... Miami's trio of LF Marcell Ozuna, CF Christian Yelich and Stanton leads all major league outfields in on-base-plus-slugging percentage. ... This is Atlanta's fourth straight losing season. ... This is Miami's eighth consecutive losing season. ... CF Ender Inciarte has 110 home hits this season, second most in Atlanta history behind Ralph Garr's 121 in 1971. Inciarte was a Gold Glove winner last year and an All-Star this season. ... Marlins LHP Adam Conley has an 11.94 ERA in five starts this month, and Miami manager Don Mattingly said he is concerned with a drop in velocity to 86 mph.