The victory improved New Jersey's record in shootouts to 7-1. And, after going 2-for-3 against the Panthers, they have now scored on 16 of 23 attempts.
When in doubt, go to the shootout.
"You've got great goaltending at one end and you've got fantastic skill on the other end," said Devils coach Peter DeBoer. "The first three guys we've shot with, we've only once or twice gone even to the fourth shooter. Those guys have been money all year."
With their goals, Kovalchuk moved to 5-for-6 this season and Elias is now 3-for-5. Zach Parise was stopped by Jose Theodore, only the second time he's failed to score in eight shootout attempts.
For the Panthers, it's just the opposite. They're now 1-4 in shootouts and have scored only one goal in 14 tries.
"There's so many different ways to analyze this," said Florida coach Kevin Dineen. "It's such a specialized way to end a game. We've lost a lot of points in shootouts. It's something we need to improve at."
The shootout capped a Devils comeback from a 2-0 deficit and served as a little payback.
The Devils blew a 3-0 lead in a 4-3 loss to the Panthers on Nov. 21 in DeBoer's return to the BankAtlantic Center.
DeBoer downplayed the significance of beating the Panthers, the team he coached for four seasons before being fired last April.
"I think we're past that," he said. "We're just trying to win games.
"I just like the way we played. I'm happy we won and I'm glad we got the two points. I think we deserved them. Even if we hadn't, I liked the way we played. We played a good team game. We pursued the puck. I thought we kept them pinned in for extended periods. It was a good effort by our guys."
Elias and Parise scored in regulation for the Devils, and Kovalchuk had two assists.
The Devils almost won the game in the final seconds of regulation, but Petr Sykora took too sharp an angle on a tip-in into an open net.
"I think we're lucky to get one (point), if you really look at it," said Panthers defenseman Ed Jovanovski. "A second left in the game, we gave up a pretty good opportunity. For a lot of the game, in our zone we had some turnovers that eventually are going to bite us in the butt. We've got to clean up those areas. We'll take the point and put it in the bank. We know as a team we can do a lot better."
Brodeur made 24 saves in regulation and overtime, but faced only one shot in the third period. He stopped Tomas Fleischmann and Versteeg in the shootout before Elias clinched the victory by beating Theodore with a wrist shot between the legs.
Versteeg's two goals in regulation gave the Panthers a 2-0 lead in the second period. He also had two goals in the earlier meeting.
"He's good," Brodeur said. "He's pretty calm with that puck. It's kind of hard to see on the first goal, but he put it in through his legs. It's impressive. He's a good player."
Versteeg, though, wasn't happy about missing in the shootout. He tried to beat Brodeur with a high wrist shot to the glove side, the same way he beat him on a breakaway in the second period.
This time, he didn't get the puck as high and Brodeur was able to snag it with his glove.
"We've thrown a lot away and we've got to be better in the shootout," Versteeg said. "Myself, when you're 0-for-4, you're not contributing in that. That's something I take pride in and I'm sure other guys do, too. You want to help the team out that way."
Even though he was beaten on two of three shootouts attempts by the Devils, Theodore nonetheless had a strong rebound outing two nights after he was pulled from a game against the Rangers.
Theodore, who gave up six goals in 22 shots in the first two periods of the 6-1 loss to the Rangers, stopped 32 New Jersey shots in regulation and overtime.
"He saved us throughout the entire game," Versteeg said. "He's the reason we got to overtime."
This was the 10th consecutive Florida home game decided by one goal. The Panthers are 4-1-5 in those games.
The Panthers have lost three in a row for the first time since they dropped three consecutive shootouts — against Winnipeg, Chicago and Tampa Bay — between Oct. 31 and Nov. 6.
"We didn't play well tonight," Dineen said. "I think that's a follow-through on our game in (New York). We looked tired. We weren't moving our feet. We didn't have much options. Not a great night for us."
Defenseman Kurtis Foster, acquired in a four-player trade with Anaheim on Monday, made his debut for New Jersey. In addition to a regular shift on defense, Foster played on the Devils' first power-play unit.
Foster got 21:53 of ice time and had four shots on goal, second-most in the game behind Kovalchuk's five.
The game was chippy throughout, especially after the first period. The teams combined for 69 hits and there were numerous scuffles after whistles.
"For me, there's just so much interference that's come back in the game," Dineen said. "You expect Kenny Daneyko to jump over the boards. It was really like a game from the '80s, it really was. There was just so much interference. That's an area that our League has taken pride, that we're trying to get the skill back into it, and that wasn't a factor tonight."
1 - 0 FLA
2 - 0 FLA
2 - 1 FLA