Hischier scored off a 2-on-1 with Palmieri at 8:06 of the third period to make it 4-2, and Noesen scored his second of the game 32 seconds later to give the Devils a 5-2 lead at 8:38.
"I was first thinking pass, but saw that I had a shooting lane and took it and [was] lucky it went in," said Hischier, who intercepted a pass deep in the Devils zone, carried the puck up the ice and scored from the right face-off circle. "I would say it gives me confidence for sure. When you're shooting, it's never a wrong decision."
Jeff Skinner and Brett Pesce scored, and Scott Darling made 17 saves for the Hurricanes (27-22-9), who had their three-game winning streak end. Carolina leads the Columbus Blue Jackets and New York Islanders by one point for the second wild card into the Stanley Cup Playoffs from the Eastern Conference.
"We didn't manage certain situations very well," Hurricanes coach Bill Peters said. "On the Hischier 2-on-1, we didn't have a forward covering there. There were some things we did to make the game harder than it needed to be and that's the stuff we've got to clean up."
Hischier assisted on Palmieri's goal that made it 3-2 with 2:32 remaining in the second period.
"I like to play in the big games," Hischier said. "I just like to play in those situations; that's when I'm having the most fun."
Noesen gave the Devils a 2-1 lead at 6:48 of the second when he scored off a rebound. Pesce scored 55 seconds later off a wrist shot from the right circle to tie it 2-2 at 7:43.