Barkov's shot from the left circle on the rush deflected in.
Paul Maurice made his debut as Florida coach in the first of two split-squad games between the teams, who will play again in Nashville at 8 p.m. ET.
Ryan Lomberg, Eetu Luostarinen and Kai Schwindt scored, and Aaron Ekblad and Santtu Kinnunen each had two assists for the Panthers. Barkov had an assist, and Sergei Bobrovsky made 10 saves on 12 shots in 31:45 before being replaced by Mack Guzda, who made 12 saves.
Juuso Parssinen had a goal and an assist for the Predators. Connor Ingram made 10 saves on 12 shots in 31:17 before being replaced by Devin Cooley, who made 18 saves.
Ryan Johansen tied it 3-3 for Nashville with 5:25 left in the third period on a deflection.
Luostarinen gave Florida a 1-0 lead with a shorthanded goal with 43 seconds left in the first period when he scored on a 2-on-1.
Schwindt made it 2-0 at 3:41 of the second period before Parssinen cut it to 2-1 at 4:42. Roland McKeown tied it 2-2 at 11:45.
Lomberg put the Panthers ahead 3-2 at 2:11 of the third on a rebound at the left side of the net.
