Just 26 seconds after Florida's Viktor Kozlov hit the crossbar on a breakaway, Hull got his second goal of the game.
"I thought I had him," Kozlov said. "It was off his feet and hit the crossbar. It was a good save."
At the other end, defenseman Jason Woolley passed to the left faceoff circle, where Hull unleashed a patented one-timer that hit goaltender Roberto Luongo's right pad and went into the net 68 seconds into the extra period.
"The ice was so bad, it was slow developing," said Hull, who is four goals shy of 700 for his career. "I just opened up for Woolley and I almost thought about not shooting it. I said, 'Just shhot it as hard as you can and hopefully it would find a hole in the net.'" "I knew Hull was on the outside," Woolley said. "It was a great shot, a powerful shot. Luongo seemed to be in pretty good position."
Luongo made 30 saves but could not stop Hull's blast.
"It was a good shot and I got a piece of it. I tried to stop the puck," Luongo said.
Pavel Datsyuk, who missed 18 games with a strained knee, set up both goals for the Red Wings, who were coming off Tuesday's 1-0 loss in Tampa Bay but improved to 5-1-3 in their last nine road contests.
After a scoreless first period, Hull ended Detroit's drought at 83 minutes, 14 seconds with his 16th goal, another hard slap shot from the low slot. He also netted the game-winner in Sunday's 4-3 overtime triumph at Chicago.
Marcus Nilson tied it for the Panthers just 51 seconds into the third period with his third goal in four games. He picked the puck out of mid-air, dropped to the ice and turned before shooting.
"I wanted to get the shot off as quickly as possible," said Nilson, who has scored in two straight games and has a four-game points streak. "I just picked it up as it was bouncing and just turned around and fired it."
Kozlov's assist extended his points streak to six games.
But neither team was able to score over the rest of regulation and Florida headed to overtime for the 20th time this season.
Manny Legace stopped 28 shots in his first start in six games for Detroit, while Luongo turned aside 30 for the Panthers, whose home winless streak reached nine games (0-3-2-4).
"I thought the breakaway was a 2-on-0, to be honest with you," Legace said. "I thought (Kozlov) was going to the low blocker side or the five-hole. I just lied down and got lucky. It hit me and then the crossbar."
"I think Legace is very underrated, not many people know about him," Hull added. "Everytime we throw him in there, he plays fantastic for us."
Florida has been a much better road team, earning at least a point in 14 of its last 15 games away from the Office Depot Center.
"In general we played a good game," Luongo said. "We can't lose in overtime, we've got to win games for us to move up. At this point of the season, every game is important for us."