Kevin Lankinen made 33 saves for the Blackhawks (15-13-5), who won for the first time in five games against the Panthers this season (1-3-1).
"We needed the win," Chicago coach Jeremy Colliton said. "We needed something good to happen to us. We probably deserved a bit better on the [road] trip (1-5-0), but that doesn't get you anywhere.
"We've got to earn some momentum, and I think we've done that, and it's up to us to do something with it."
Noel Acciari had two assists, and Chris Driedger made 29 saves for the Panthers (20-8-4), who played without center Aleksander Barkov because of a lower-body injury.
The teams play here again Thursday.
"You lose a key guy, but it's a good test on the whole group there," Florida coach Joel Quenneville said. "But the impact he has on the team, it was noticeable there. We started to get our way as the game progressed, more so later in the third, but it was a tough, tough start."