Stephen Weiss, Richard Zednik, Nathan Horton and Cory Stillman scored for the Panthers, who improved to 13-4-3 since Jan. 1 and moved into sixth place in the Eastern Conference.
Zednik and Weiss both added an assist, while Michael Frolik and David Booth each had two assists.
Scott Clemmensen made 24 saves for New Jersey.
The Atlantic Division-leading Devils lost for only the third time in 16 games. Their road winning streak was tied for longest in the NHL this season. Boston won seven in a row on the road from Dec. 12-Jan. 15.
The Devils had won the first two meetings between the teams, 3-1 at New Jersey and 3-2 at Florida.
The loss matched New Jersey's most lopsided of the season.
Vokoun, who made his seventh consecutive start in goal, recorded his 30th career shutout. His best save came in the third period on a New Jersey power play when he quickly slid to his right to stop Brian Gionta's one-timer.
Vokoun got some help in the first period when defenseman Johnny Oduya's slap shot from the point bounced off the goal post to his right.
The Panthers blew the game open with two goals in a span of 2:28 in the second period.
Leading 1-0, the Panthers got only their second power-play goal in their last 26 opportunities when Zednik scored at 11:27. After Clemmensen stopped Frolik's wrist shot, the rebound went off Booth's stick and right to Zednik, standing alone at the side of the net.
Horton made it 3-0 at 14:05 after Booth's pass from behind the net went off a skate. Horton grabbed the loose puck in front, held it as he skated to his left and then fired a wrist shot over Clemmensen's right shoulder.
Stillman closed out the scoring with 2:54 left in regulation when he one-timed Weiss' centering pass.
Weiss opened the scoring at 4:18 of the first when he grabbed a rebound in the high slot and fired a wrist shot that went in off the post.
Notes: Florida improved to 8-0 on Tuesdays and to 21-1-1 when leading after two periods. ... New Jersey played without injured RW Brendan Shanahan (foot) and D Paul Martin (upper body) for the second consecutive game. ... New Jersey's road winning streak was the second- longest in franchise history behind a 10-game run in the 2000-01 season. ... The game began a stretch when Florida plays a division leader in five of seven games.