The Mets had scored in the first inning but didn't manage a hit after the fourth inning until Nieuwenhuis ended the game. Miami pitching retired 11 straight before a walk in the eighth.
Justin Turner worked Bell for a 13-pitch walk that forced in the tying run.
After a ground out, Nieuwenhuis sent a drive to deep right for the game-winning single.
Ramon Ramirez, who pitched two innings for two-hit relief, improved to 2-1 with the win.