They haven't been to the postseason since, but they took another step toward wrapping up a playoff berth, jumping past idle Pittsburgh and Philadelphia into fourth place in the East with 93 points.
Corey Potter and Dan Girardi scored for the Rangers. They held a 38-23 shots advantage but have lost four of six.
But just when this game seemed headed to overtime, LaRose and Brind'Amour turned a 2-2 game into a comfortable win for Carolina.
LaRose broke a 2-all tie when he took a feed from Jussi Jokinen as he skated across the net and tapped it past Henrik Lundqvist with 7:35 remaining. The crowd had yet to settle down after that goal when Brind'Amour made it a two-goal game by beating Lundqvist with a wrist shot from the left circle.
Cam Ward, making his career-best 25th straight start, improved to 17-6-2 in that stretch by turning aside 36 shots. Lundqvist stopped 19 shots for the Rangers before he was pulled for an extra attacker.
LaRose briefly put Carolina up 2-1 midway through the second with a pretty tap-in of Ray Whitney's rebound, before Girardi tied it at the 5½-minute mark when he beat Ward with a slap shot on the power play - only the Rangers' third goal in 34 chances with the man advantage.
Staal gave the Hurricanes an early lead about 4½ minutes in on their first power play - and just their second shot on goal - of the night. He unloaded a hard slap shot from behind the circle that appeared to click off younger brother Marc Staal's skate and past Lundqvist for his team-leading 35th goal.
Potter's first career goal tied it with 2½ minutes before the first break, a slap shot from the right point that got past a screened Ward - who was being pestered by noted antagonist Sean Avery. It was New York's first goal this season in Raleigh; Ward shut them out 3-0 on March 9.
The Rangers controlled much of the early action this time, outshooting Carolina 13-3 largely because the Hurricanes, the NHL's least-penalized team, were whistled four times during an intense, physical opening 20 minutes. But as the Rangers' power-play struggles mounted, so did their frustration, with an agitated Gomez at one point slamming his stick into the ice.
Notes: LaRose rang the crossbar with a wrist shot about 20 seconds before his goal. ... New York RW Ryan Callahan has points in three straight games. ... Carolina RW Scott Walker returned after missing 11 games with an upper-body injury. ... Rangers D Michal Rozsival missed his fifth straight game with an injured left leg. ... The Rangers got an early scare when Lundqvist collided with Hurricanes C Tuomo Ruutu midway through the first. The goalie sprawled on the ice and flexed his left arm for a few minutes, but stayed in the game.
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