Tuukka Rask stopped 38 shots for the defending Stanley Cup champions.
Jason Garrison and Shawn Matthias scored goals for Florida, and Scott Clemmensen made 33 saves.
Bergeron also had a goal in the shootout for Boston, and Stephen Weiss had a shootout goal for Florida.
RED WINGS 5, SABRES 0
In Detroit, Henrik Zetterberg scored the first of Detroit’s three goals in the opening period and the Red Wings broke a franchise record with their 15th consecutive home victory with a win over Buffalo.
It is the longest single-season winning streak by an NHL team at home since 1976 when Philadelphia won 20 in a row to match a league mark set by Boston during the 1929-30 season, according to STATS, LLC.
BLUES 1, STARS 0
In St. Louis, Jaroslav Halak made 22 saves for his third shutout of the season and T.J. Oshie scored midway through the third period as surging St. Louis stayed unbeaten in 2012.
JETS 2, SENATORS 0
In Ottawa, Chris Mason made 25 saves for his second shutout and Winnipeg ended a three-game losing streak with a win over Ottawa.
COYOTES 6, AVALANCHE 1
In Glendale, Ariz., Shane Doan and Boyd Gordon scored two goals apiece and Phoenix returned from an 0-3 road trip to rout Colorado.
Gilbert Brule had a goal and assist for the Coyotes just six days after he was claimed off waivers from Edmonton.
PREDATORS 3, ISLANDERS 1
In Uniondale, N.Y., Sergei Kostitsyn and Matt Halischuk scored on Nashville’s first two shots against Islanders goalie Kevin Poulin, and the surging Predators rolled to a win.
The Predators won for the eighth time in nine games and are 14-4 in their past 18.