The Hurricanes won their seventh straight game and jumped past both Pittsburgh and Philadelphia into the No. 4 seed in the Eastern Conference playoff race. Carolina has just four games remaining in its regular season while Pittsburgh has five and Philadelphia six.
New York, meanwhile, dropped into eighth place in the playoff chase. Montreal, which defeated the New York Islanders Thursday, moved one point in front of the Rangers.
The Rangers, who have four games remaining, are two points ahead of ninth-place Florida.
New York twice rallied from one goal behind, but LaRose put the Hurricanes in front for good with 7:35 to play. Brind'Amour followed 28 seconds later.
Cam Ward made 36 saves to win his seventh in a row.
Henrik Lundqvist allowed all four Carolina goals on just 23 shots.