Kyle Palmieri and Blake Coleman each scored twice, and Mackenzie Blackwood made 27 saves for the Devils (18-20-7), who won consecutive games for the first time since winning three straight from Dec. 27-31.
"There are things in our game plan that we didn't execute and weren't detailed enough on," Palmieri said. "You're not going to score eight goals every night. There's definitely some stuff to tighten up, but it was good we found a way to win."
WATCH: [All Blackhawks vs. Devils highlights]
Patrick Kane extended his point streak to six games with two goals and two assists for the Blackhawks (16-23-9). Cam Ward allowed six goals on 25 shots in two periods, and Collin Delia made 14 saves on 15 shots in relief.
"[The game] is one that you throw in the trash and move on," Chicago captain Jonathan Toews said. "You remind yourself what makes you a good team. That's work ethic, commitment to the little things, winning your battles, getting pucks deep and making things difficult for the other team. When we get back to doing that, we're going to get the results."
Kane tied it 1-1 with a power-play goal 3:07 into the second period before the Devils scored five times to take a 6-1 lead.
Palmieri scored on a breakaway at 5:16 and on the power play at 8:27 to make it 3-1. Travis Zajac got it to 4-1 at 10:07, Sami Vatanen scored a power-play goal at 14:58 to make it 5-1, and Kevin Rooney scored his first NHL goal in his 11th game at 17:58 for a 6-1 advantage.