Dickey (19-6) yielded a pair of runs on six hits to became the first Mets pitcher since Frank Viola and Dwight Gooden in 1990 to win at least 19 games in a season.
The knuckleballer -- who lowered his National League-best ERA to 2.67 -- took a 4-0 shutout into the ninth inning. He was pulled after allowing a walk to Greg Dobbs and a Donovan Solano double to begin the frame.
Jon Rauch relieved and was greeted by John Buck with a three-run homer to make the game close, but he managed to close out the victory for his fourth save and the Mets clinched their three-game series.
Jason Bay socked a two-run homer and Scott Hairston added a solo shot for New York.
Marlins starter Mark Buehrle (13-13) was touched for four runs on five hits over six frames.