Aho cut it to 3-2 at 15:58 of the third when his shot deflected in off the stick of Rangers forward Lias Andersson, but Adam Fox scored into an empty net with 1:25 remaining to make it 4-2.
Panarin gave the Rangers a 1-0 lead with 28 seconds remaining in the first period, receiving a pass from behind the net by Strome and scoring with a one-timer from the slot.
"We talked about it before the game actually, how we should hang around the middle a bit more," Strome said. "It only takes him a split second. What a shot, right off his stick before anyone can react."
Carolina outshot New York 22-6 in the first period, which included two power-play opportunities for the Hurricanes.
"They freeze you and go side to side, and they're there for rebounds," Lundqvist said. "So the only thing I had in my head was not to be overaggressive to the shooter, and I had to be ready for the second shot. There was a couple times I got lucky. I was doing a lot of good things, but I also got some bounces."
Hamilton tied it 1-1 on a redirection of Jaccob Slavin's point shot in the slot at 14:32 of the second period.