Toews also had a goal and an assist in regulation, and Drake Caggiula also scored for the Blackhawks. Corey Crawford made 38 saves and stopped both of Florida's shots in the shootout.
''Would have loved to close it out in regulation,'' Blackhawks coach Jeremy Colliton said. ''That would have been easier on everyone.''
Mike Hoffman had a goal and an assist, and Mike Matheson also scored for the Panthers. Sergei Bobrovsky stopped 27 shots.
The Panthers have lost six straight home games. Their last home win was a 4-3 victory against the Los Angeles Kings on Jan. 16. The Panthers are 0-5-1 at home in February. They salvaged a much needed point.
''Tough loss, but we'll take the point and move in the other direction,'' coach Joel Quenneville said.
The Panthers are five points behind Toronto and three behind Columbus in the wild card race in the Eastern Conference.
Down 2-1, the Panthers tied it when Matheson scored on a wrist shot from the right circle with 1:28 left in the third.
''We felt good about our odds going into overtime,'' Matheson said. ''We created a lot of chances going into overtime. It's frustrating not to see them go in.''
The Blackhawks are 4-4 in overtime.
''You never want to give up one late and have to take it to overtime,'' Crawford said. ''We had some chances, off the bar, kind of went back and forth, but it was nice to get that win in the shootout.''
Caggiula broke a 1-all tie after he deflected a shot by Connor Murphy from the blue line and into the net at 6:21 of the second.
The Panthers took a 1-0 lead when Hoffman skated in on a breakaway and backhanded the puck past Crawford 4:07 in. Hoffman leads the Panthers with 27 goals.
The Blackhawks tied it at 1 when Toews redirected a shot from above the right circle by Adam Boqvist and into the net at 12:54 of the first.
NOTES: Blackhawks F Brandon Hagel was recalled from AHL Rockford on an emergency basis. ... The game was Panthers coach Quenneville's second against his former team. Florida won 4-3 in Chicago on Jan. 21.
Blackhawks: host Anaheim on Tuesday.
Panthers: host Calgary on Sunday.
More AP NHL: https://apnews.com/NHL and https://twitter.com/AP-Sports
Copyright 2020 by STATS LLC and Associated Press. Any commercial use or distribution without the express written consent of STATS LLC and Associated Press is strictly prohibited.