Sergei Brylin and Jamie Langenbrunner also scored to help the Devils break out of a collective scoring slump.
The struggling power play keyed the outburst. After going 2-for-29 with the man advantage in the previous five games, the Devils went 3-for-7 against the Panthers.
Martin Brodeur made 18 saves for the Devils, winners of four straight and six of the last seven.
Stephen Weiss and Chris Gratton scored for the Panthers who dropped their third in a row.
Elias, mired in a deep slump, opened the scoring at 5:36 by knocking in a rebound for his third goal. The Devils' captain had gone five games without a point and the tally was only his second in the last 14 games.
Parise gave the Devils a 2-0 lead at 17:02, taking a pass from John Madden and whipping the puck past Eddie Belfour.
In the second, Brylin scored on a 5-on-3 power-play opportunity to give the Devils a 3-0 lead at 1:27.
Florida's Weiss countered with a score at 6:46 before Langenbrunner closed out the scoring in the period at 11:50.
In the third, Gratton roofed a hard shot from the left circle under the crossbar at 8:02 to trim the New Jersey advantage to 4-2.
Notes: Gratton returned to the Panthers after missing Friday's 5-4 overtime loss in Buffalo for the birth of his second child. ... The Devils extended their home winning streak over the Panthers to five. ... The Devils made shorter work of the Panthers after shootout victories in their last two.