The contest was knotted 3-3 in the sixth inning when the Braves erupted for four runs, ignited with Johnson smashed a pitch down the right field line to send home Justin Upton and Freddie Freeman with two outs.
Upton finished 3-for-4 with an RBI and three runs scored while Brian McCann also supplied three hits and drove in a pair for National League East-leading Atlanta, which posted a fourth straight victory.
Andrelton Simmons knocked in two runs as well, including an RBI triple, as the Braves pounded out 16 hits.
Kris Medlen (6-7) posted his fifth victory in six starts, handling the Marlins on three runs over six innings. The right-hander allowed nine hits, walked two and struck out one.
Miami reliever Dan Jennings (0-1) absorbed the loss, coughing up three runs without recording an out.
Logan Morrison hit a two-run homer in the Marlins' defeat.