B.J. Upton opened the first with a double and scored on a Justin Upton sacrifice fly to give the Braves a one run edge, but most of the damage came in a four run bottom of the second.
Tommy La Stella added an RBI single to right field, but just when it looked as if Eovaldi would escape the inning, Freddie Freeman hit a three run home run to left to push Atlanta's lead to five.
Eovaldi eventually settled in, pitching seven innings and giving up five runs while walking and striking out two Braves. Atlanta was aggressive early in counts and took advantage of first pitch strikes over the heart of the plate.
Ervin Santana, on the contrary, was dominant for the Braves. In seven and a third innings, Santana gave up one run while walking three and striking out ten.
Miami's lone run came in the third, when Christian Yelich took a first pitch fastball to right field for an RBI single with runners on first and third and one out.
Gerald Laird drove in a run against Sam Dyson to make it a 6-1 contest, and the Marlins couldn't put together a late rally.
Miami still has a chance to win the series with a game four victory on Thursday.
Hero of The Game: Christian Yelich (+.054 WPA)
Goat of The Game: Nathan Eovaldi (-.289 WPA)
Play of The Game: Freddie Freeman homered in the second, allowing B.J. Upton and Tommy La Stella to score. (+.165 WPA)