Aaron Ekblad scored his 10th goal of the season, and Sergei Bobrovsky made 26 saves for the Panthers (19-5-4), who rallied with five unanswered goals for their sixth win in seven games.
"[Barkov] stepped up at the right time as usual," Bobrovsky said. "He's definitely a special player. I think he's the best player in the world. He does so many things behind that nobody can see. He's so valuable for us."
Patrick Kane scored for the Blackhawks (14-11-5), who have lost four of five. Kevin Lankinen made 30 saves.
Chicago was 0-for-8 on the power play in the two-game set; Florida won 4-2 here Saturday.
"It's a good reminder of what it takes to win in this league," Lankinen said. "Every team is good, it's not easy to win. We can't let the game slip away for five seconds or five minutes, it's going to cost you. We're learning that the hard way now. In the long run we'll mature, learn from this and be an even better team coming up."
Barkov, who also had two assists, scored Florida's first shorthanded goal of the season with 6:34 remaining off a rebound after he won a face-off in the Panthers zone to make it 4-3.
"It's too bad, because I think a lot of guys for a lot of the night were really good," Blackhawks coach Jeremy Colliton said. "What happened at the end of the night on the power play was inexcusable and tough to explain how that happens. We're close, but ultimately the difference was at a key moment of the game, we weren't up to the task."
The win moved the Panthers into a tie with the New York Islanders for the most points in the NHL (42). It's the first time Florida has been first in the NHL standings after the second game of the season since Dec. 28, 1996 (20-8-9, 49 points).
"We're just a different team this year, and I think the League is starting to notice that," Panthers defenseman MacKenzie Weegar said. "We deserve all the credit that we're getting right now. It's fun to be in South Florida."
Kane capitalized on a turnover and gave the Blackhawks a 1-0 lead at 10:38 of the first period.
