The Rangers grabbed home-ice advantage in the Eastern Conference quarterfinal series with Callahan, Sean Avery and Nigel Dawes scoring in the final 20 minutes to break open what had been a tight battle.
The outcome continued a season-long trend involving these teams. The Rangers defeated the Devils in seven of their eight regular-season meetings.
Game 2 of the best-of-seven series will be played Friday in New Jersey.
Callahan scored 7:23 into the third period and Avery gave the Rangers some insurance with 2:53 to play. Dawes added an empty-net goal with five seconds remaining.
Celebrity Families of 2014 [PHOTOS]