Steve Bernier and Ilya Kovalchuk also scored and Martin Brodeur made 14 saves for New Jersey, which squandered a two-goal lead and had fans dreading another first-round playoff exit until Zajac scored from the right hand circle.
The shot beat Scott Clemmensen to the lower corner and set off a mob scene on the ice.
Clemmensen was outstanding, stopping 39 shots in an emergency start for the injured Jose Theodore. Kris Versteeg and Sean Bergenheim tallied for Florida, which was looking for its first series win since 1996.
Game 7 will be played in Sunrise, Fla., on Thursday.
Two other series in the conference are also headed to Game 7s. Washington will be at second-seeded Boston tonight and Ottawa will be at the top-seeded Rangers on Thursday.
The Panthers had a chance in a scramble in front of Brodeur just before Zajac’s goal. However, Zajac pulled the puck away from the crease and led a rush up ice. Zach Parise took his cross-ice pass and gave the puck to Kovalchuk, who found Zajac skating down the right wing for a shot along the ice into the net.
The Devils outshot Florida 42-16 in a game played before a sellout crowd.