Brian Gionta had a goal and an assist while Patrik Elias added three helpers for the Devils, who have won four straight games. Scott Clemmensen made 26 saves in the win.
Ryan Malone, Martin St. Louis and Radim Vrbata each had a goal for the Lightning, who have dropped six of their last seven games. Olaf Kolzig started in net, but was pulled in the second period after allowing five goals on 28 shots. Karri Ramo finished the game between the pipes and stopped 15-of-17 shots.
The Devils scored just 1:44 into the contest as Anssi Salmela wristed a shot from the left point that Mike Rupp redirected between the pads of Kolzig from the left circle.
On a delayed penalty call, the Devils took a 2-0 lead as Zach Parise, on the ice for the extra attacker, took a pass from Jay Leach near the top of the left circle and blasted a shot into the net through a screen with 2:23 left in the first.
A bit under two minutes into the second, Zubrus made it a 3-0 game as his slap shot from the left circle handcuffed Kolzig.
At the 4:34 mark of the second, Zubrus got his second goal of the game when he knocked in the puck during a scrum in front of the net.
Gionta made it a 5-0 game with 8:21 left in the second as his shot from a sharp angle at the left side got past Kolzig, who was pulled from net and replaced by Ramo.
The goaltending change sparked the Lightning as the team scored the next three tallies to make it a two-goal game.
Vaclav Prospal battled along the backboards and came out front with the puck. From the right side of the net he threw the puck across the goalmouth where Vrbata tapped it past Clemmensen with 6:52 left in the second.
St. Louis scored 1 1/2 minutes later as a loose puck popped out to the right side and he banged it in for the 500th point as a member of Tampa Bay.
Malone was awarded a penalty shot with 3:18 to play as he was hauled down on a breakaway and he made it count, as he snapped a shot past the glove of Clemmensen to make it a 5-3 contest.
Zubrus completed the hat trick 7:21 into the third as he skated in on a breakaway and slipped a backhand past a stretched-out Ramo for a 6-3 lead.
With 5:22 left in the game, Gionta had the puck behind the net and centered it for Zubrus, who calmly wristed it under the glove of Ramo.