Eric Staal set the club record for career shots on goal, passing Hall of Famer Ron Francis late in the second period. Staal finished with four shots, giving him 2,542.
Anton Khudobin stopped 34 shots in his 16th straight appearance for Carolina.
Nick Bjugstad scored for Florida, which enters the Olympic break having lost five of six.
Tim Thomas stopped just 10 of the 14 shots he faced. He was pulled with 15:24 left in the second after Tlusty tapped in a rebound to make it 4-1.
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