Marisnick was playing in his ninth big league game and his solo shot broke a scoreless tie.
Placido Polanco and Giancarlo Stanton both had a sacrifice fly in the third to give the Marlins a 3-0 lead and Henderson Alvarez then teamed with two relievers to protect the advantage.
Alvarez (2-1) gave up both New York runs on six hits through 7 1/3 innings. Chad Qaulls retired one batter in the eighth and Mike Dunn recorded the final four outs for his second save.
Jenrry Mejia (1-1) took the loss, allowing all three Miami runs on six hits in six frames.