Brind'Amour started the decisive sequence when he took the puck from Florida's Bryan Allen at the blue-line. The Carolina captain skated in alone on Craig Anderson and slipped the puck between his legs.
David Tanabe scored twice, and Erik Cole and Eric Staal added third-period goals to help Carolina rally from a three-goal deficit for the second time this season on home ice against Florida.
Olli Jokinen scored his team-leading 39th goal and added two assists. Ville Peltonen also had a goal and two assists for Florida, which was denied its first victory on Carolina's ice since 2002.
Martin Gelinas scored his 300th career goal, Jay Bouwmeester also scored and Nathan Horton added two assists for the Panthers.