Jack Hughes tied the game 1-1 before the period's end, bringing a puck towards goal from the corner and eluding a Corey Crawford poke check and firing a shot top corner at 14:46 of the first.
P.K. Subban gave the visitors the lead in the opening minute of the middle frame, firing a slap shot from the point through traffic and into the net at 0:51.
The Devils took a 3-1 lead at the 7:22 mark of the second as Damon Severson walked into the slot from the side boards and slid a shot between the legs of Crawford in tight.
Former Blackhawk and Chicago native John Hayden scored his first of the season in his former home at 10:40 of the second, walking into the zone and beating Crawford from the top of the circle with a wrister for a 4-1 lead. Robin Lehner would replace Crawford in goal for Chicago after the goal.
Travis Zajac made it a 5-1 lead before the period's end with a shorthanded tally off the rush. Lehner made an initial stop on Blake Coleman's shot, but Zajac was on the doorstep to put the puck past the sprawled Blackhawks goale at 17:22.
Blake Coleman would find the net 18 seconds into the third period, sneaking behind Duncan Keith and firing a shot while falling down on a partial breakaway to give New Jersey a 6-1 lead.
New Jersey made it 7-1 as Pavel Zacha fired a shot from the high slot past a mass of bodies in front at 18:21 of the final period.