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.
Notable deaths of 2014 [PHOTOS]
UPI Sports Results for September 19, 2014