Kreider got the Rangers within 2-1 at 4:30 of the second period, redirecting Trouba’s shot from the point past Kochetkov.
Jordan Martinook made it 3-1 at 6:32 after a giveaway by Shesterkin. Jordan Staal got the puck and centered it to Martinook in front of the net.
"It's hard to chase a game against that team," Kreider said. "They are pretty good with the lead. ... They had a game plan, they stuck to it."
Jalen Chatfield extended it to 4-1 at 1:33 of the third period when his shot beat a screened Shesterkin.
Svechnikov made it 5-1 at 2:56 on a breakaway, shifting the puck from backhand to forehand and beating Shesterkin from in front.
Svechnikov and Aho have combined for 24 points over the past five games.
"They have been dominant," Skjei said. "I don't think there's any way else to put it. They've been our best players and just on fire the last week or so. It's fun to watch and I just try to get them the puck."
Michael Bunting took a pass in front from Brendan Lemieux, shifted the puck around Shesterkin and put it into an open net at the right post at 15:49 for the 6-1 final.
"I think we are capable of more, but again, they're a good team that plays big and strong and physical; they don't make a lot of mistakes, and they didn't," Rangers coach Peter Laviolette said.
The Hurricanes were 2-for-4 on the power play and 3-for-3 on the penalty kill after finishing the month of December with the top penalty kill in the NHL (93.8 percent) and the second-best power play (36.7).
"I think we were good early. Had a good plan," Hurricanes coach Rod Brind'Amour said. "I think just in general, certainly we've come together as a group [on special teams]. Obviously, it helps on the penalty kill when your goalie is making some big saves to kind of right the ship for us. It's been a good stretch."
Kochetkov made 21 saves over the first two periods. He is 6-1-2 with a 1.86 goals-against average and .934 save percentage in his past nine starts, allowing two or fewer goals in seven of those games.
"'Koch' has been amazing," Svechnikov said. "I feel like every game, he gets more confidence and he's just been better and better to be honest, but he is already elite so it's exciting to see him be huge for us."
NOTES: Svechnikov, who also had a five-game multipoint streak last season, became the fourth player in Hurricanes/Hartford Whalers history with multiple five-game multipoint streaks, joining Kevin Dineen (six games in 1988-89; five games in 1984-85), Ron Francis (five games in 1987-88; five games in 1986-87) and Mike Rogers (six games in 1979-80; five games in 1980-81). … With an assist on Kreider's goal, Artemi Panarin extended his point streak to five games (six goals, two assists). … Kreider scored his 166th goal at home (regular season and playoffs) to surpass Rod Gilbert for most at the current Madison Square Garden. … Carolina forward Jesper Fast did not play after sustaining an upper-body injury in a 3-2 win against the Toronto Maple Leafs on Saturday. He was replaced by Lemieux, who had an assist in 8:53 of ice time.