Bergeron's breakaway score midway through the final frame forged a 2-2 tie and forced a scoreless overtime.
In the shootout, Bergeron gave Boston the advantage in the second round by faking Reimer to the ice and sliding the puck into an open net.
Tuukka Rask preserved the win with a third-round save on Nikolai Kulemin and the Bruins emerged with a home-and-home split against the Maple Leafs.
Milan Lucic also scored and Rask finished with 23 saves in the victory.
Kulemin and Joffrey Lupul found the net for Toronto, which dropped a fifth straight in Boston.
Reimer stopped 27-of-29 shots for the Leafs.
Celebrity Families of 2014 [PHOTOS]