Moments after Panthers goalie Roberto Luongo stopped Henrik Zetterberg from the edge of the crease, Florida caught Detroit in a line change. Jonathan Marchessault's long pass sent Barkov in on a breakaway, and he slipped a backhand past goalie Petr Mrazek.
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"I don't even remember my last goal, so it was good to see one go in," Barkov said. "That made the win feel even better."
The goal was Barkov's first since he scored against Mrazek on Oct. 15 (21 games). He has three this season.
"His game has been coming along for a few nights now," Rowe said. "He's a horse, and he scored a great goal in overtime."
Red Wings coach Jeff Blashill said he was frustrated by rookie defenseman Ryan Sproul, who dumped the puck onto Marchessault's stick before going for a change.
"There are always going to be chances when it is 3-on-3, but that was a play we can't make," Blashill said. "We have cut down our turnovers and mistakes recently, but we went backward in the last two games."
Luongo made 20 saves; Mrazek made 28. The Panthers are 5-0 in overtime; the Red Wings are 1-3.
Detroit took advantage of an Aaron Ekblad turnover to take a 1-0 lead at 1:23 of the first period. Ekblad's between-the-legs pass hit Barkov's skate and bounced to Zetterberg, who beat Luongo with a high backhand.