Gagner made it 2-1 at 3:13 of the second period, deflecting in Troy Stecher's shot for his second goal of the season.
The Red Wings blocked 23 shots, including six in a 38-second stretch late in the third period.
"That was awesome," Nedeljkovic said. "The guys were sacrificing their bodies, and the crowd was really getting into it. The fans fed off it and we fed off the fans."
Moments later, Suter tied the game with 2:41 left in regulation, scoring his first goal with the Red Wings.
"They have become a really tough team to play," Brunette said. "The way they are going, with the kids they have in their system, they could really become a problem for us."
Barkov finished off a 2-on-1 break with Jonathan Huberdeau in overtime to make the Panthers the first team to win their first eight games since the Montreal Canadiens won their first nine start the 2015-16 season.
"[Barkov] got a huge face-off win in the [defensive] zone, I got the puck back to him and then I let the big guys get to work," Panthers defenseman MacKenzie Weegar said. "I was just a decoy, watching an incredible pass from [Huberdeau] to [Barkov]."
NOTES: Barkov has scored 32 points (13 goals, 19 assists) in 32 games against the Red Wings, his most against any team. … Bobrovsky is 6-0-0 with a .944 save percentage. … Red Wings rookie defenseman Moritz Seider had an assist, giving him seven points -- all assists -- in eight NHL games. … Duclair's assist on Barkov's first goal was his 200th NHL point (94 goals, 106 assists in 404 games).