Improving to 27-23-6, Florida now sits just one point out of a playoff spot.
"We go back-to-back, but we get to feel good tonight," Panthers head coach Paul Maurice said. "We'll get a little more sleep in the morning, and everyone's excited for the game tomorrow [at St. Louis]."
Following a scoreless first period, the Panthers opened the scoring in the second when Eetu Luostarinen tipped a shot from Gustav Forsling past Filip Gustavsson to make it 1-0 at 2:06.
Having a breakout season, Luostarinen has now matched the career-high 26 points (12 goals, 14 assists) he posted last season, needing 22 fewer games to hit that mark this time around.
Just over three minutes later, the Wild pulled even when Kirill Kaprizov sniped an wicked shot past Bobrovsky from the left circle to make it 1-1 at 5:15 for his 30th goal of the campaign.
Making more than a few highlight-reel stops in the middle frame, Bobrovsky's biggest save came just past the midway point of the period when he denied Matt Boldy on a breakaway.
That was just one of nine high-danger saves for Bobrovsky during the game.
"I feel great," said Bobrovsky, who's gone 8-3-1 with a .919 save percentage over his last 13 starts. "Everybody pulled the rope in the same direction, and it's so much fun to be part of it."
On an early power play in the third period, Brandon Montour appeared to break the tie and put the Panthers on top, but the goal came off the board due to incidental contact with the goalie.
With the action eventually getting to overtime, Bobrovsky made three saves in the extra frame, including stretching out to absolutely rob Jared Spurgeon of a goal with roughly 12 seconds left on the clock.