Necas, who also had two assists, won it for the Hurricanes when he one-timed a pass from Sebastian Aho near the right goal post.
"It feels good; you just end the game," Necas said. "It's a good feeling, especially for me, I really like 3-on-3 (in overtime); there's a lot of space. You can make some skilled plays."
Vincent Trocheck tied the game with 1:33 left in the third period, and Alex Nedeljkovic made 44 saves for the Hurricanes (14-6-1), who swept the two-game set. Carolina won 4-3 in the shootout here Saturday when Necas scored the game-winner in the fifth round.
"It's always good to win no matter how you do it," Hurricanes coach Rod Brind'Amour said. "Obviously that's not how you would draw it up. The third period was a little shaky for us. We were on our heels.
"But I love how our guys are digging in. They seem to never quit. It looked like that was going to go the other way tonight, and we bounce back. It's two points, and we'll take them."
Frank Vatrano scored for a third straight game, and Eetu Luostarinen also scored for the Panthers (13-4-4), who have lost consecutive games for the first time this season. Chris Driedger made 28 saves.
"It looked like we were in a pretty good spot to win the game, but I like the way we're competing," Florida coach Joel Quenneville said. "There were a lot of positives coming out of the game even though we were trailing."
Trocheck tied it 2-2 with Nedeljkovic off for an extra attacker. It was Trocheck's third goal in three games this season against the Panthers, who traded him to the Hurricanes on Feb. 24, 2020, for four players, including Luostarinen.
Trocheck leads Carolina with 11 goals.
"He's done it for us all year," Brind'Amour said. "He's logging a lot of minutes, plays every situation now. It was a huge acquisition at the time; I think we talked about it, getting a player like that. You're seeing that now. His play this year has been great."