Dickey (8-1) turned in his eighth straight start without a loss, striking out nine en route to the victory, which followed Johan Santana's no-hitter in the first game of the series.
The knuckleballer tossed 73 of his 100 pitches for strikes and lowered his ERA to 2.69 as the Mets improved to 16-9 against National League East opponents.
Dickey also drove in a run, while David Wright went 2-for-4 with a solo homer for New York.
St. Louis starter Lance Lynn (8-2) lasted 4 2/3 innings, allowing three runs (two earned) on five hits while issuing four walks.
The Cardinals dropped their fourth straight.