Tuomo Ruutu added two assists to help the Hurricanes snap a two-game losing streak.
Brandon Prust scored for New York, coming off a 7-0 home victory over Toronto on Wednesday night.
Henrik Lundqvist made 35 saves for the injury ravaged Rangers. One day after finding out Brandon Dubinsky (stress fracture in left leg) and Ruslan Fedotenko (separated left shoulder) would miss extended time, New York struggled to keep up with Carolina offensively.
The Hurricanes struck early in the first period when LaRose deflected Jeff Skinner's shot through Lundqvist's legs. The spinning puck looked as if it might stop before crossing the goal line, but it had enough momentum to make it over. Carolina made it 2-0 with 5:17 left in the period when Jokinen deflected Joe Corvo's slap shot from the blue line past Lundqvist on a power play.
Early in the second period, Sergei Samsonov fed a streaking Sutter near the New York blue line to send Sutter in on a partial breakaway. Sutter went to his backhand to beat Lundqvist for his first goal in 16 games.
Prust spoiled Ward's shutout with 8:20 left in the game when he snapped a wrist shot past Ward's glove from the slot. Skinner finished the scoring with 4:09 remaining.
It was an important win for the Hurricanes, who entered the night three points behind Atlanta in the chase for the final playoff spot in the Eastern Conference. Coming into the game, Carolina only had five wins all season against the eight teams ahead of it in the Eastern Conference.
NOTES: The Rangers hit the post twice in the opening minutes of the game. ... Prust was favoring his left hand after a fight with Carolina's Jay Harrison in the second period.