Adam Gaudette scored on a rebound to give Chicago a 1-0 lead at 13:47 of the first period. It was his first goal since being traded to the Blackhawks by the Vancouver Canucks on April 12.
Wennberg tied it 1-1 at 7:47 of the second period on a redirection of a shot by Weegar for a power-play goal.
"We were definitely back to doing what we need to do when we play with puck support and speed and active [defensemen]," Panthers coach Joel Quenneville said. "We got up the ice a lot better, and all of the sudden we got some zone time. I think that was the difference. We didn't have much pace in the first."
Vinnie Hinostroza scored on a 2-on-1 with Brandon Hagel to give Chicago a 2-1 lead at 10:09 of the second. Anthony Duclair tied it 2-2 on a rebound in front at 13:09.
"Yeah, obviously pretty much all of our games we've had some good and we've some bad spurts," Hinostroza said. "I think it just comes down to putting a full 60 minutes together. If we do that, we're harder to play against, we're harder to beat.
"But once again, we never gave up. We had some great opportunities in the third, great opportunities in overtime. It's a step in the right direction, but we'd like to get two points there."
NOTES: Panthers forward Patric Hornqvist missed his third game because of an upper-body injury. … Florida forward Grigori Denisenko scored his first NHL point with an assist on Duclair's goal. … Hinostroza has scored 10 points (three goals, seven assists) in his past 11 games.