Brodeur had a shutout going until he missed a shot by Chris Kreider early in the third period, finishing up the winning performance with seven saves in the final frame.
Adam Henrique also scored for the Devils, who took the first match-up of the season against their rivals from New York and improved to 2-1 in February.
Henrik Lundqvist turned aside 19-of-22 shots for the Rangers.
Video of Victoria’s Secret models trying to 'twerk' hits Instagram
Costly malfunction causes beer flood at Boston-area brewery