Gustav Forsling and Sam Reinhart scored for the Panthers, the second wild card in the East.
Alex Lyon allowed three goals on 26 shots before being relieved 8:32 into the third period by Sergei Bobrovsky, who made eight saves in his first game since March 27.
"It had nothing really to do with (Lyon)," Florida coach Paul Maurice said about pulling his starting goalie. "He's played heavy-pressure games and a lot of them. And at 3-0, in my mind, if we mount a comeback, it's not because our goalie stands on his head. We've got to get some action going.
"And I've got another goalie -- who's a really, really good goalie -- that hasn't played in a long time. There's a risk, right? You put a guy in who's been sitting for a while, but he needs a little bit of action. That's all that was. It was not a critique of Alex's game."
Panthers defenseman Aaron Ekblad initially left at 11:11 of the second period after colliding with Charlie McAvoy in Boston's zone. Ekblad returned and played two shifts, but did not return for the third period. There was no update after the game.
Hall gave the Bruins a 1-0 lead at 2:26 of the first period with a wrist shot from above the right face-off circle that went off Lyon's glove.
"I thought what set the tone was Charlie McAvoy laying a big hit in the first shift (on Eetu Luostarinen) and that was kind of a telltale sign of the night and how hard we were gonna play," Hall said. "And the first period, whether your score or not, you want to dictate play and you want to play Bruins hockey; I thought we did that. "
Charlie Coyle made it 2-0 at 6:00 of the second period when he tipped in a shot from the top of the right circle by Brad Marchand.
Pastrnak extended it to 3-0 at 8:32 of the third period with a wrist shot from the left circle after taking a stretch pass from Orlov, and Nick Foligno made it 4-0 at 11:45 when he went forehand-backhand after taking a centering pass from Hall.
