Vaclav Prospal and Dan Boyle also scored and Johan Holmqvist had 21 saves in bouncing back from a bad game against the Rangers to lead the Lightning to their 12th win in 15 games.
Scott Gomez scored for the Devils, who had won four in a row. The loss was only their third in regulation time in the last 21 games (15-3-3).
Tarnasky, who played less than two minutes on four shifts in the first two periods, got his first career winning goal at 17:24, stuffing a shot past Martin Brodeur at the right post after poking the puck off the stick of defenceman Brad Lukowich.
Lecavalier matched his career high with his 35th goal less than a minute later with Tampa Bay having an extra skater for a delayed penalty on New Jersey. Prospal found Lecavalier with a pass above the left circle and he ripped a shot just inside the post for a 3-1 lead.
Boyle gave Tampa Bay more breathing room, scoring his 12th of the season 56 seconds into the third period on a power play.
Lecavalier set up Prospal's tying goal 44 seconds into the second period, sending a pass from behind the net to his linemate all alone in front of Brodeur.
Gomez got a lucky goal 2:12 after the opening faceoff on a power play. His shot from a bad angle deflected off Tampa Bay defenceman Cory Sarich and eluded Holmqvist, who was pulled in the second period of a 5-0 loss to New York on Friday night.
Against the Devils, only a bad bounce beat him. His biggest save came shortly after the Gomez goal, when he stopped Patrik Elias breaking in all alone.
Notes: Tampa Bay is 2-1 against New Jersey this season, and 13-4 against the Atlantic Division . . . The loss was only the Devils fifth at home in regulation this season (20-5-4) . . . The Lightning are 31-4-2 when they score three or more goals . . . Lecavalier also scored 35 goals last season . . . New Jersey centre John Madden missed the final 6:28 of the first period after being cut on the right side of his face by a shot.