Kane recorded a goal to stretch his points streak to 12 consecutive games as Chicago improved to 6-1-2 in its last nine contests.
Bryan Bickell added a score and Nick Leddy supplied a goal and an assist for the Blackhawks.
Antti Raanta needed to make just 10 saves.
Michael Ryder and Stephen Gionta each notched a goal for the Devils.
Cory Schneider turned aside 32-of-37 shots.