Henrik Lundqvist made 33 saves and the Rangers ended a three-game losing streak.
The Rangers struck early and late with power-play goals in the opening period for a 2-0 lead.
Hurricanes defenseman Brett Pesce tripped Rick Nash at 1:04, and it took the Rangers only 5 seconds to cash in. Zuccarello drilled a shot over Cam Ward from the top of the left circle to extend his points streak against Carolina to 11 games.
Lindberg doubled the Rangers advantage with 1:37 left, whipping a one-timer past Ward from the slot off a cross-ice feed from Dan Boyle.
Both teams got two goals in the second period, and Ward was his own worst enemy as the Hurricanes tried to battle back.
Jordan Stall put Carolina on the board at 1:40 from the slot, deflecting a backhand feed from Andrej Nestrasil.
Ward gave it right back. Kreider beat him from a sharp angle at the bottom of the right circle only 44 seconds later.
In frustration and anger, Ward smashed his goal stick against the right post.
Kevin Hayes took a tripping penalty with 6:17 left in the second, and the Hurricanes nearly scored when Justin Faulk hit the post. Instead, New York killed the penalty, and Hayes skated out of the box, picked off Ward's clearing attempt and set up Brassard's goal with 4:11 left.
Rask scored with 2:01 left, and then Terry made it 4-3 8:23 into the third by sliding the puck under Lundqvist on a semi breakaway.
NOTES: Rangers center Derek Stepan will miss four to six weeks because of broken ribs. New York coach Alain Vigneault made the announcement following the morning skate. New York recalled forward Jayson Megna from Hartford of the AHL. ... C Jordan Stall played in his 200th game for the Hurricanes. ... Carolina's lone scratch was D Michal Jordan. The Rangers scratched Megna and D Dylan McIlrath. ... Celebrities at the game included actress Susan Sarandon and Jets quarterback Ryan Fitzpatrick. ... Rangers D Kevin Klein suffered a muscle strain in the first period and did not return.