Brad Richards had two goals and an assist as 2, at Madison Square Garden.
Marian Gaborik added a goal and an assist while Carl Hagelin finished with a goal and two helpers for the Rangers, who earned their second straight win.
Tim Brent and Drayson Bowman tallied goals for Carolina, which ended a five- game road trip with a 2-2-1 record. Cam Ward made 24 saves in the loss.
New York struck just 3:02 into the game. Dan Girardi's slap shot from the right point when high and wide but took a strange carom off the boards and wound up right on the stick of Gaborik to the left of the net, where he lifted it in before Ward could find the puck.
Richards gave the Rangers a two-goal edge at the 10:12 mark of the second period with a snap shot from the right circle that snuck under the crossbar on the short side.
He made it 3-0 just under three minutes later when he received a pass to the right of the net from Hagelin, cruised into the slot waiting for Ward to go down and wristed a shot over the prone goaltender.
However, the Hurricanes responded with two quick goals of their own.
The first came on the power play with 5:16 left in the middle stanza when Eric Staal's shot from the right circle was stopped in a crowd, but Brent swiped the puck towards the net out of a scrum and it slipped under the right arm of Biron.
Only 32 seconds later, Carolina broke down the ice after a New York offensive-zone turnover. Brandon Sutter's one-timer from the right circle was partially blocked by New York's Derek Stepan, but the puck skipped right to Bowman at the right of the net and he stuffed it home to make it a one-goal margin.
But Hagelin stole an errant pass by the Hurricanes' Tuomo Ruutu behind the Carolina net and finished with a wraparound to the right side with seven minutes left in the game to give the Rangers back their two-goal cushion.
Biron made nine saves in the third period to lock up the victory.
The Hurricanes have now lost five straight to the Rangers, including all four in this year's series...New York improved to 24-7-2 at home, while Carolina fell to 9-16-9 on the road this season...Carolina went 1-for-4 on the power play...The Rangers were 0-for-3 with the man advantage.