Aube-Kubel scored from a sharp angle to give Philadelphia a 3-1 lead at 4:28, and Couturier popped the rebound of a Jakub Voracek shot over Nedeljkovic's glove at 4:54 to make it 4-1.
"Puck's bouncing at the blue line, we backcheck, we get sticks on it, puck finds a way to find their guy backdoor (on Williams' goal)," Couturier said. "We didn't deviate from the way we want to play. The next line went out there and gained momentum again. That just shows the maturity of our team."
The Flyers have a plus-25 goal differential in the third period this season (85-60) after they were even in the third last season (90-90).
"If you look at our lineup this year compared to other years, we're maybe a little more experienced," Couturier said. "We've got some young guys that are taking big steps forward, maturing in their game. It just shows the evolution of our team over the past few years. I just think we're more responsible with our decisions. We've just got to keep doing that."
Brind'Amour said he could feel the Hurricanes going the wrong way after Williams' goal.
"The next shift after it, we had two turnovers again in the neutral zone ... we just didn't do it right after we scored," he said. "We got away from how we were playing. It's unfortunate. It was our younger guys too. They're trying hard, just that's where they've got to buckle down a little better."
Hurricanes captain Jordan Staal said the veterans are to blame too.
"We've got to be better, to a man, including myself," he said. "It's got to be more, and we need everyone. We need the whole team ready to go and engaged, right from the start."
Ivan Provorov scored on his own rebound to give Philadelphia a 1-0 lead with 1:37 remaining in the first period.
