Jesper Bratt scored two goals for the Devils (44-16-6), who are 7-1-1 in their past nine games.
New Jersey moved into a tie with Carolina, which has one game in hand, for first place in the Metropolitan Division.
"I think we feel like we've been doing a good job and we've worked extremely hard for this," Bratt said. "It's been a lot of hard, tough years. That brings us even more motivation that we want even more. I think when we're playing a game like this, we just get excited for what's ahead."
Pyotr Kochetkov made 20 saves for the Hurricanes (43-14-8), who were shut out for the second time in two days.
"You tip your hat, but we just handed them two points," Carolina coach Rod Brind'Amour said. "That's what happened, and then maybe they didn't have to do anything after that. We played hard all night. I thought we were in control. You just can't give a good team like that (that much)."
Carolina played without forward Andrei Svechnikov, who sustained a lower-body injury in a 4-0 loss to the Vegas Golden Knights on Saturday.
"We're playing hard and we're getting our chances," Hurricanes defenseman Jaccob Slavin said. "We just got to just continue and get those chances and play the right way to get those chances. So, I don't know if it's a slump, necessarily, but we'll get out of it."