Ryan McDonagh scored to stretch his scoring streak to four games, and Keith Yandle also had a goal for New York.
Joakim Nordstrom scored for Carolina, and Eddie Lack made 28 saves.
New York has won 14 of its last 15 meetings with Carolina.
The game was played before a tiny crowd -- many in Rangers jerseys -- due in part to several inches of wet snow that began falling in the afternoon.
New York led 2-0 after a dominant first period, outshooting the Hurricanes 17-9 and recording 18 hits to the hosts' six.
McDonagh put the Rangers ahead with 5:59 left in the first, stealing John-Michael Liles' pass at the red line and beating Lack on a rocket over the right shoulder from the left circle.
Yandle made it 2-0 with 2:07 remaining in the first by beating Lack over the right shoulder off Oscar Lindberg's pass from behind the goal line.
Nordstrom beat Lundqvist on a one-timer from Andrej Nestrasil 3:29 into the second.
Miller made it 3-1 on a shot from the left circle at 9:41, then scored again 2:10 later after stealing the puck from Jaccob Slavin in the slot and working it past Lack stick side.
NOTES: This was the opener of a three-game homestand for Carolina, with Calgary visiting on Sunday night and Chicago on Tuesday night. ... The Rangers were not able to fly out after the game because of weather conditions. They're scheduled to play at Ottawa on Sunday. ... Carolina C Riley Nash (illness) was out while teammates LW Chris Terry and D Michal Jordan were healthy scratches. ... Rangers C Chris Kreider (neck) was out. Dylan McIlrath was a healthy scratch. ... Daniel Altschuller dressed as the Hurricanes' backup goalie for the second straight game with Cam Ward (concussion) on injured reserve.