The Panthers twice rallied from one goal down, but were blanked in the final period by Johan Hedberg.
Kovalchuk gave the Devils a 3-2 lead with 8:20 to play by tipping in a shot from Patrik Elias. New Jersey added two empty net goals in the final minute, one from Kovalchuk and another from Zach Parise.
The Devils ended a two-game skid and handed Florida its second straight loss.
Hedberg made 22 saves, giving up a goal in the first period to Mikael Samuelsson and in the second to Krys Barch.
Jacob Markstrom, making his seventh start of the season and the eighth of his career, gave up three goals on 27 shots.