The Devils won their second straight game after having lost four in a row.
Paul Martin put a wrist shot past Tomas Vokoun at 5:49 of the third and Gionta then took advantage of a turnover in Florida's end of the ice to score his fourth goal of the season and give the Devils a 3-0 lead.
Clemmensen lost his bid for a shutout when Michael Frolik scored his first NHL goal on the power play with 11:18 to play.
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