Jones and Freeman each stroked a two-run double to lead the Braves to their eighth win in their last nine games. Jason Hayward counted an RBI single among his three hits.
Cristhian Martinez (5-2) was credited with the win in relief of Mike Minor, whose start was limited to 3 2/3 innings due to a 42-minute rain delay.
The rain didn't come soon enough for Marlins starter Nathan Eovaldi (2-7), who was hung with the loss after allowing six runs on eight hits in two innings.
Atlanta pounced on Eovaldi with three runs in the first inning, two of them on Jones' double. The Braves added two more in the second on Freeman's RBI double.