The Blackhawks let a two-goal lead get away but Corey Crawford came through with a perfect shootout after stopping 41 shots in regulation and overtime.
Chicago has won three in a row and four of its last five. The Panthers have dropped two straight.
Stephen Weiss started the Florida comeback with 1:41 to go in the second and Ed Jovanovski's tip-in with 2:04 left in regulation forced extra time. It was the fourth straight game in which the Panthers had scored in the final three minutes of regulation, but they won just one of those contests.
Jacob Markstrom took the loss while making 31 saves.