Teddy Purcell and Victor Hedman scored in the shootout, while Mathieu Garon stopped both New Jersey attempts, as Tampa Bay scored a comeback 5-4 victory over the Devils on Friday.
Steven Stamkos added two goals and assisted on the game-tying tally from Alex Killorn for the Lightning, who received a goal from Nate Thompson and 21 saves from Garon to give Jon Cooper a win in his head-coaching debut.
"It's just a wave of emotions," Cooper said on earning his first win. "It's all like it happened in slow motion."
Andrei Loktionov, Andy Greene, Tom Kostopoulos and Ryan Carter scored for the Devils, who have lost five of their last seven outings.
Martin Brodeur stopped 21 shots in defeat.
Purcell opened the game's final segment by scoring with a wrister, then Garon forced a Travis Zajac chance wide at the right post. Hedman whipped one past Brodeur, and Patrik Elias didn't get his shot off after Garon used a poke check to knock the puck away.
Loktionov registered the game's first goal with 5:50 played in the second period, and Kostopoulos followed with his first for New Jersey 51 seconds later on a penalty shot -- a chance that resulted from Hedman dragging him down on a breakaway.
Stamkos and Thompson tallied 2:26 apart to tie the game, but Greene's power- play marker 1:32 later put the Devils back on top.
Carter's short-handed goal at 2:39 of the third gave New Jersey a 4-2 advantage, then Stamkos netted his 25th of the year at 7:11 to make it a one- goal game once more.
Garon was pulled for an extra skater in the final minute and the move paid off with 16 seconds remaining as Killorn one-timed a Stamkos feed from the right circle to force overtime.
The Devils survived a holding call to defenseman Matt D'Agostini early in the extra session.
"It's disappointing when you're 15 seconds away from getting two points," Devils head coach Peter DeBoer said. "We'll just put our one point in the bank and keep moving forward."
Tampa Bay evened its 2013 shootout slate to 1-1, while New Jersey fell to 2-6 ...Stamkos picked up his fourth multi-goal effort of the season and scored at least three points for the fifth time in this truncated schedule ... Tampa defenseman Andrej Sustr, a former Nebraska-Omaha product, made his NHL debut ... Carter's marker was the Devils' ninth short-handed goal of the year, best in the league ... Kostopoulos notched his first free-shot goal on his third career penalty shot.