The Panthers trailed 1-0 after the first period but outshot the Red Wings 28-14 in the final two periods.
"When the other team scores the first goal, we usually struggle, kind of back on our heels," Huberdeau said. "But we were able to get the tying goal."
"This is one of the toughest buildings to play in. We wanted to play with energy. They had to play last night [a 3-1 win in New Jersey]," Panthers coach Peter Horachek said. " ... We just wanted to work both ends of the rink."
Daniel Cleary scored for Detroit, which is only 5-6-6 at home.
"I thought it was lack of energy for sure. You try to fight through it the best you possibly can," Red Wings coach Mike Babcock said. "We had a game last night, they sat in our building, hung out and waited for us. There's no excuse for anything, you got to find ways to win games. "
Backup goalie Jonas Gustavsson, making his second consecutive start, made 35 saves. It was Gustavsson's first regulation loss of the season (8-1-1).
"It's always a little bit tougher to play that back to back, you got to be smart, save your legs and all that. We played a team that played good tonight, made it tough for us," Gustavsson said.
"I felt like they were skating and forechecked us pretty good. At the end of the day we probably could have gotten a bounce and scored that second goal. You never know. We just got to bounce back from this and have a good next game."
Huberdeau gave Florida the lead at 3:29 of the third period. Left wide open in front of Gustavsson, Huberdeau put in a backhand shot after making a move for his seventh goal.
Hayes tied it at 1 at 2:59 of the second period with his third goal of the season.
Gustavsson appeared to have a shot by Matthias smothered. But the puck dropped under one of Gustavsson's pads and Hayes poked it in for his second goal in two games.
The Panthers outshot the Red Wings 17-5 in the second period.
"Our game plan was just to play hard and we refocused during the game," Hayes said.
Niklas Kronwall talked about what happened to Detroit after the first.
"We stopped skating. I don't think it has anything to do with the energy. I don't know what it is," he said. "We have to be a lot more desperate and determined than that. We stopped skating and started watching hockey instead of playing."
Cleary opened the scoring 4:06 into the game with his first goal in 24 games. He put in the rebound of Justin Abdelkader's shot for Cleary's second goal of the season.
Detroit C Stephen Weiss played his first game against his former team. Weiss signed a five-year, $25 million free agent contract with the Red Wings in July. ... Detroit remained without both C Pavel Datsyuk (concussion) and captain Henrik Zetterberg (herniated disc). The team said that Datsyuk will return on Tuesday when the two teams play in Florida. ... Panthers goalie Tim Thomas is from Flint, Mich., which is about 60 miles north of Detroit. ... The Red Wings were also without C Darren Helm, who missed his second game with a shoulder injury.