Miami, which began the day a half-game ahead of two teams in the NL wild-card race, has allowed 25 runs in losing its last three games. The Marlins dropped to 2-7 against Atlanta this year.
The Braves improved to just 12-32 at Turner Field. They have the NL's worst overall record, the majors' worst home record and the least productive offense in the big leagues, but they took a 6-3 lead in the sixth.
Jeff Francoeur's double chased Marlins starter Wei-Yin Chen, and Mike Dunn gave up Erick Aybar's RBI infield single, Snyder's two-run go-ahead triple and Chase d'Arnaud's RBI single.
Chen (4-3) allowed eight hits, four runs, two walks and struck out two in 5 1/3 innings. The left-hander has a 7.27 ERA over his last five starts.