The Hurricanes converted two of theirs -- and Cam Ward frustrated the Rangers.
"There are certain games that are going to be exciting, and there are certain games that are going to be dogs," Carolina coach Paul Maurice said. "For whatever reason when the Hurricanes and the Rangers play, I think they're very exciting games and lots of chances and just outstanding goaltending."
Tuomo Ruutu added two assists to help the Hurricanes snap a two-game losing streak.
Ward had his highest number of saves in more than a month.
"He's our wall back there," LaRose said. "A lot of times when we make mistakes, he bails us out and they don't get noticed as much. He's definitely our leader, and we try to play well in front of him."
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.
"They got off to a good start," New York defenseman Marc Staal said. "We obviously opened up the ice a little bit too much for them. At the same time, we were getting a ton of chances, too. We were just unable to bury one."
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.
"I thought the third goal was the biggest one," New York coach John Tortorella said. "That's a simple rush. It's not an odd-man rush -- we allow it to turn into an odd-man rush. So we were sloppy defensively."
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 had only five wins all season against the eight teams ahead of it in the Eastern Conference.
"What I thought you saw tonight was a real good look at the leadership in our room," Maurice said.
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.