"Sometimes it just happens like that," Hunt said. "It's kind of ironic that we both get it in the same game. He's such a good friend of mine. To see him get it and follow it up with mine was pretty special."
Aleksander Barkov and Jonathan Huberdeau each had a goal and an assist, and Aaron Ekblad and MacKenzie Weegar each had two assists for the Panthers (30-27-12), who have won two in a row after losing six straight (0-2-4) and are seven points behind the Columbus Blue Jackets for the second wild card into the Stanley Cup Playoffs from the Eastern Conference.
WATCH: [All Red Wings vs. Panthers highlights]
"[Huberdeau and I] just try to hold each accountable and try to bring the best out of each other," Barkov said. "We're playing with a really good player, too, [Evgenii] Dadonov. As a line, we try to push each other more and more every shift and try to control the game and play with the puck. We're having fun, so we'll just try to continue."
Sam Montembeault made 19 saves for his second consecutive victory.
Thomas Vanek scored, and Jimmy Howard made 37 saves for the Red Wings (24-35-10), who are 1-7-3 in their past 11 games and were outshot by Florida 43-20.
"They just had Grade A chance after Grade A chance," Vanek said. "Pretty fun night for them, pretty awful for us."
Brown, playing in his 24th NHL game, gave the Panthers a 1-0 lead at 6:42 of the first period on a wrist shot from the high slot off a pass from Troy Brouwer.
"It was incredible," said Brown, whose goal was his first point in the NHL. "I definitely have more of a defensive mind-set. I didn't know if it was going to happen this season or whatever, but just thrilled and relieved that I got it out of the way."
Jamie McGinn scored a power-play goal to make it 2-0 at 9:22, getting the rebound of Ekblad's initial shot at the top of the crease.