Barkov had a second-period assist that gave him 614 points (238 goals, 376 assists), passing Jonathan Huberdeau (613 points; 198 goals, 415 assists).
"He might be the most humble man I've ever met, and he's certainly the most humble elite player I've ever met," Florida coach Paul Maurice said.
Matthew Tkachuk had a goal and two assists for his 31st multipoint game this season, tying Huberdeau's Florida record set in 2018-19.
Carter Verhaeghe scored twice, and Sergei Bobrovsky made 20 saves for the Panthers (36-27-7), who have a seven-game point streak (6-0-1). Florida moved into the second wild card from the Eastern Conference, one point ahead of the Pittsburgh Penguins, who lost 2-1 to the Ottawa Senators on Monday.
"Getting into a playoff spot was our goal, but we still have a lot of work to do," Verhaeghe said. "We've got the right guys in this room, a lot of good leadership and a lot of great players."