Heisey started the game-winning sequence in the 11th with a leadoff single against Carlos Zambrano (7-10), who then issued a walk to Joey Votto.
That brought up Ludwick, who scorched a grounder through the hole to chase home Heisey from second base with the decisive run.
Logan Ondrusek (4-2) was credited with the win after wiggling out of a 10th-inning jam and Jonathan Broxton nailed down the triumph with his second save with the Reds.
The victory allowed National League Central-leading Cincinnati to avoid a three-game sweep.
Gregg Dobbs supplied a two-run triple for the Marlins.