With the second line continuing to cook, the Panthers added an insurance goal when, after a big hit from Bennett separated a Bruins player from the puck, Tkachuk scooped up the rubber and set up Carter Verhaeghe for a snipe from the left circle to make it 4-2 at 7:00.
Sending many fans to the exits, Montour buried a slap shot from the point to make it 5-2 at 12:30.
"We just kept on the gas," Montour said. "They're a heck of a team, so you don't want to let up. I don't think we did. We got a nice goal to start and we just kept building on that."
After Luostarinen cashed in on an empty net to extend Florida's lead to 6-2 at 17:35, Taylor Hall squeaked in a shot to make it 6-3 at 18:50. Earning the first playoff win of his NHL career, Lyon, who's been Florida's late-season unsung hero, finished with 34 saves on 37 shots.
In the opposing crease, Ullmark surrendered five goals on 29 shots.
"It was fun," Lyon said. "I really enjoy playing in that atmosphere. It's fun for me. I get energized. It was just a good time. I'm happy we got the win. Very talented, very good opponent. Now is not the time to take our foot off the gas. I think that's where our focus has to be."