Brandon Hagel scored, and Kevin Lankinen made 31 saves for the Blackhawks (14-10-5), who have lost three of their past four games.
Chicago and Florida will complete the two-game set here Monday.
"I still think it's positive in here," Hagel said. "Teams are going to have that throughout the year, every team does from good teams to bad teams. Every team goes through these stretches. We still have confidence in here. We know we're a good hockey team. Just regroup, get back to it and get back to the way we know how to play and good things will happen."
Hagel scored 28 seconds into the second period on a give-and-go with Dominik Kubalik to give Chicago a 1-0 lead.
Barkov tied it 1-1 at 7:46 on his rebound after Blackhawks defenseman Duncan Keith couldn't clear the puck out of the zone.
"I mean, he's elite," Duclair said of Barkov. "He's one of the best centermen in the League, probably one of the best two-way forwards I've ever played with. [He's] just so skilled, so talented and just very happy to be playing with him, obviously. Me and Carter [Verhaeghe], we just try to do our best to help him out in any situation, and just very happy that we found some chemistry early on in the season and it keeps going right now."
Duclair, who had the primary assist on the play, began the game on the fourth line before being reunited on the top line with Barkov and Verhaeghe.
"[Duclair] had good speed in that first period there," Panthers coach Joel Quenneville said. "We didn't want to change the lines, but I wanted to get him back to the lineup and he earned that opportunity based on how he was skating. … They all played a part in all the goals that they scored. Nice to see they get reunited and have a big night as well. So it was a good to have him back, and I thought that his speed was very dangerous."