Brind'Amour scored his ninth goal of the season on the power play at 9:52 of the first period, and then scored his 10th goal at 2:44 of the third, as Carolina forged a 2-0 lead. He got assists from four different players, while goalie Cam Ward stopped 27-of-28 shots, as the Hurricanes ended a two-game skid.
Florida's lone tally came from Nathan Horton on the power play at 13:59 of the third.
Goaltender Tomas Vokoun stopped 31-of-33 shots for the Panthers, who have lost six of their last eight games.
On the power play, Carolina went 1-for-2, and Florida went 1-for-5.
Carolina left wing Glen Wesley played in his 1,400th game, to become only the 26th player in NHL history to reach that milestone.