Barkov had a goal and an assist to finish with 96 points (35 goals, 61 assists) and break the record set by Pavel Bure in 1999-00 (94 points; 58 goals, 36 assists).
"Of course it means a lot, and it's awesome, and I want to thank everybody who played with me," Barkov said. "Without those guys it wouldn't be possible."
WATCH: [All Devils vs. Panthers highlights]
Travis Zajac won it with a power-play goal 56 seconds into overtime. He scored on a wrist shot after Jonathan Huberdeau was called for delay of game at 19:59 of the third period.
Nathan Bastian scored two goals for the Devils (31-41-10), who were 4-2-1 in their last seven games of the season. Bastian came in with one goal in six NHL games. Mackenzie Blackwood made 37 saves.
"It's pretty wild," said Bastian, who made his NHL debut Jan. 19. "Coming into the game, seeing the lineup, I was gifted with some pretty good linemates. My mindset was I had quite the task in front of me, having to play against some pretty good players on the other side. Seeing [linemates] Nico [Hischier] and [Blake Coleman], I just wanted to make the most of my opportunity there."