The contest was tied 1-1 after the first period after Olesz and traded goals with the Blackhawks' Dave Bolland.
Bolland scored the equalizer after winning a struggle involving several players for possession of a loose puck. The Blackhawks center backhanded the puck into the open net with only 30 seconds left in the period.
Zednik and Bouwmeester scored in the second to give Florida a 3-1 advantage.
Zednik's ninth goal of the season, at 6:25 of the second, broke a 1-1 tie and turned out to be the game-winner.
In a mammoth effort, goaltender Tomas Vokoun stopped 44 of 45 shots for the Panthers, who had lost five of previous seven games.
Patrick Lalime stopped 21 of 24 shots for the Blackhawks, have dropped six of their last seven.
There were no power play goals on 11 combined chances.