Mattias Ekholm cut it to 3-1 at 12:23 on a slap shot from the point. It was his fourth goal in the past four games.
Ekblad made it 4-1 on the power play at 18:44.
Forsberg cut it to 4-2 on a redirection at 19:34.
Ekblad scored another power-play goal from the top of the slot on the rush to make it 5-2 at 9:07 of the third period.
"We always want [defensemen] in the rush," Ekblad said. "[Quenneville] is a big believer and pushes us to do that every night. I've just been trying to move my feet. I say it to myself before every game, 'Skate, skate, skate.' It's been working this year. I think that's the basis of it all, just moving my feet and trying to put myself in good positions."
Colton Sissons cut it to 5-3 at 12:40.
Ryan Johansen, who came out of NHL COVID-19 protocol Thursday, pulled Nashville within 5-4 with 1:13 left and Rinne pulled for the extra attacker.
Florida killed off all 1:45 of a 5-on-3 power play in the second period.
The Predators had a goal by Rocco Grimaldi overturned at 1:58 of the third after Quenneville challenged for offside. And Forsberg had a goal disallowed at 14:30 of the third because of a slashing penalty on Nashville defenseman Roman Josi.
"We come out and we're slow, they're obviously playing way better than us in the first," Forsberg said. "That kind of puts yourself in a bad spot. After that, I think in the second period, we were starting to play the right way. And obviously in the third again, desperation kicks in and we're playing great. We're creating chances and had a couple more chances that could've went in, two goals that were disallowed. We've just got to play like that from the start."
NOTES: Panthers defenseman Anton Stralman did not play in the third period. Quenneville said he is day to day with a lower-body injury. … Predators forward Matt Duchene left the game with an undisclosed injury after taking one shift in the third. There was no update. … Nashville forward Brad Richardson had an assist and played 13:09 in his return after missing 14 games with a lower-body injury.