Scott Walker, Cory Stillman and Justin Williams also scored, and Eric Staal added two assists for Carolina. Williams' goal was his team-leading 18th of the season and seventh in seven games.
Nathan Horton scored two goals for Florida, and his second cut it to 3-2 with 4:11 remaining.
The Panthers pulled goalie Alexander Auld in the final minute, but Stillman made them pay by scoring an empty-net goal on a backhand from the blue line while falling down with 40 seconds left.
Cam Ward made 26 saves for the Hurricanes, who won their seventh straight home game against Florida.
Horton extended his points streak to five games for the Panthers, who haven't won at the RBC Center since a 2-0 victory on Dec. 6, 2002. Auld stopped 26 shots.
Brind'Amour's goal came in the opening seconds of the third period during a 4-on-3 power play.
Ray Whitney passed to Staal in the right circle, and his shot grazed Brind'Amour, who was positioned near the goal. Officials upheld the score after a brief review, giving the Carolina captain his 12th goal of the season and making it 2-1.
Walker then made it a two-goal game with about seven minutes remaining when he beat Auld high with a short wrist shot from the slot.
Horton gave Florida an early lead when he skated in from the right side and beat Ward with a wrist shot on just his team's second shot on goal. The Panthers then clamped down on defence, holding the Hurricanes without a shot for an 11-minute stretch to close the first period.
Williams tied it at 1 with about 5 minutes left in the second. Williams skated down the left side, caught Auld watching Staal approaching from the right and snapped a short wrist shot past him, extending his points streak to eight games.
Notes: Carolina leads the season series 2-1. ... The Hurricanes improved to 8-0-1 in their last nine at home against Florida. ... Horton now has 100 career points. ... Tempers flared midway through the second period when Carolina's Craig Adams and the Panthers' Steve Montador fought near the boards.