Parise scored his fifth and sixth goals of the post-season, and Gomez blocked a shot and chased down the loose puck before skating in to blow the winner past goalie Johan Holmqvist with 7:06 left in the extra period to give the Devils a 4-3 victory and tie the Eastern Conference series at two games apiece Wednesday night.
Game 5 is Friday night at New Jersey.
Brodeur had 30 saves, but squandered a two-goal lead in the second period. He has given up 12 goals in four games after entering the post-season with a career 1.89 goals-against average in 153 playoff games.
Vincent Lecavalier, Martin St. Louis and Eric Perrin scored the Lightning, who rallied from a 3-1 deficit. Holmqvist stopped 33 shots after making 64 saves in Tampa Bay victories in Games 2 and 3.
Brodeur's outstanding post-season history, and Holmqvist's NHL playoff inexperience, are the main reasons most people feel the Devils had a big advantage in the series. But the three-time Stanley Cup champion hasn't delivered the kind of performance New Jersey is accustomed to getting this time of year.
The Devils turned the puck over in their defensive zone, setting up Perrin's goal that made it 1-1 with just under eight minutes remaining in the opening period. Parise countered with his first goal for a 2-1 New Jersey lead, and the Devils went up two goals when the 22-year-old scored again on a power play midway through the second.
It wasn't enough for Brodeur to finish the job, though.
Lecavalier and St. Louis scored within a five-minute span to make it 3-3 heading into the third period. Both teams had several opportunities to win it in regulation, however Brodeur and Holmqvist were able to weather the surges.
In overtime, Gomez got in front on a Tampa Bay shot from the point, gathered the puck and broke down the ice on a 2-on-1. He ended the game and evened the series with a perfectly placed wrist shot over Holmqvist's shoulder and into the far upper corner of the goal.
Notes: The Devils outshot the Lightning 37-33, including 29-28 in regulation. ... New Jersey D Colin White sat out for the second straight game because of a stiff back. ... Lightning C Brad Richards had an assist on St. Louis' goal, giving him at least one point in 13 consecutive playoff games, a streak that began during the 2004 Stanley Cup finals.