Dickey (17-4) limited the Marlins to five hits with three walks and seven strikeouts. Prior to Friday, Cincinnati's Johnny Cueto had been the only pitcher in the major leagues with 17 victories.
It was Dickey's second win in a row, but two of his losses this season came during the month of August.
Ike Davis accounted for all three New York runs, producing a sacrifice fly in the fourth and hitting a two-run homer in the seventh.
Nate Eovaldi (4-10) suffered the loss, allowing three runs on four hits in seven innings.