Opening the scoring for the Panthers, Gustav Forsling fired a shot on net that caught a piece of Barkov's leg and sailed past Sam Montembeault to make it 1-0 just 2:37 into the first period.
On the power play, Barkov then made history when he took a pass from Sam Reinhart and rifled a shot into the cage from the right circle to make it 2-0 at 11:50. Surpassing Scott Mellanby for the most power-play goals in franchise history, it was his 67th career tally with the extra attacker.
Answering for the Canadiens, Arber Xhekaj blasted a one-timer past Sergei Bobrovsky from inches below the blue line moments after Montreal's power play expired to make it 2-1 at 14:14.
Becoming just the sixth different player in franchise history to score three goals in a single period, Barkov capped off his fourth-career hat trick when he jumped on a loose puck on the doorstep and backhanded it over Montembeault to extend Florida's lead to 3-1 at 15:22.
"It feels like I got some bounces there," Barkov, humble as ever, said when asked about his early scoring spree. "Playing with really good players, they're going to find me. That's about it."
Making it a one-goal game heading into the first intermission, Josh Anderson followed up on a shot from Mike Hoffman and cashed in on the rebound to trim Montreal's deficit to 3-2 at 19:13.
Giving the Panthers their two-goal cushion back early in the second period, Matthew Tkachuk expertly tipped in a point shot from Brandon Montour on the power play to make it 4-2 at 6:22.
Set free after a great stick lift from Colin White, Carter Verhaeghe helped the Panthers pull away even further in the third period when he shrugged off a defender and roofed a shot over Montembeault's blocker into the top of the cage to increase the advantage to 5-2 at 4:14.
"That's the way we want to play," said Verhaeghe, who leads Florida with 18 goals. "Early in the season I think we sat back on a lot of leads. It was encouraging to see that we kept going."
Not taking their foot off the gas, Tkachuk lit the lamp for a second time when he potted a rebound on the power play to make it 6-2 at 7:24. Matching a career-high with his ninth goal of the season, Eetu Luostarinen then scored on a 2-on-1 with Sam Bennett to make it 7-2 at 9:31.
Stopping all 11 shots he faced in the third period, Bobrovsky finished with 25 saves.
"We know what we need to do, and we want to do it again," Verhaeghe said. "We want to play the same way, win or lose. We want to stick with our game and try and build it. It's a good one tonight, but we've got to keep going here."
