Brendan Smith scored a shorthanded goal, and Sebastian Aho had a goal and an assist for the Hurricanes, the No. 1 seed in the Metropolitan Division.
Igor Shesterkin made 20 saves for the Rangers, the No. 2 seed in the Metropolitan.
"You get your team prepared to play, you play as hard as you can and you hope you win these hockey games," New York coach Gerard Gallant said. "I'm happy with the way we performed overall. I wish we would have got one of these two games, we probably could have. That's the way it goes. Play well, play hard, we'll find a way to get another win."
RELATED: [Complete Hurricanes vs. Rangers series coverage]
Smith made it 1-0 at 15:54 of the second period when he drove to the net on a 2-on-1 and redirected a pass from Aho with Carolina killing a four-minute penalty after Brady Skjei was called for high-sticking. Teuvo Teravainen began the play by chipping the puck to Aho off the boards into the neutral zone.
"[Teravainen] makes great plays and he can chip it into space, where I saw [Aho] moving," Smith said. "I tried to get going as fast as I could and find the lane. [Aho] is an elite passer, and he put it right on the money, so I can't take too much [credit], but it was a good read by a lot of players."
Aho scored into an empty net for the 2-0 final with two seconds remaining.
New York was 0-for-4 on the power play.
"I'm seeing a great penalty kill put a lot of pressure on them," Gallant said. "We didn't find the inside man very often in the slot, the bumper guy. They put on a lot of pressure, and we just didn't adjust to it quick enough. We've got to compete a little harder, I think."