Boqvist scored on a breakaway at 2:05, beating Panthers goalie Sergei Bobrovsky stick side.
Charlie Coyle and Charlie McAvoy scored, and Linus Ullmark made 29 saves for Boston (46-17-15), which has won four straight and is five points ahead of Florida in the Atlantic.
The Bruins swept the season series from the Panthers, winning all four games by a total of five goals.
Matthew Tkachuk and Aleksander Barkov scored, and Bobrovsky made 26 saves for Florida (48-24-6), which has lost nine of its past 12 games (3-7-2).
Tkachuk gave the Panthers a 1-0 lead 37 seconds into the game, taking advantage of an odd bounce off the end boards when the puck fell to him on the inside edge of the right circle.
McAvoy tied it 1-1 at 5:42 of the first period, beating Bobrovsky from the high slot.
The Bruins failed to capitalize on three power-play opportunities in the first period, but Coyle scored on the man advantage at 15:45 of the second period, redirecting Brad Marchand’s centering pass at the doorstep to give Boston a 2-1 lead.
Barkov tied it 2-2 at 5:24 of the third period, scoring off a rebound of Sam Reinhart’s shot from the left side with the teams skating at 4-on-4.
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