After Bergeron beat Olie Kolzig, Tim Thomas snuffed a shot by Matt Pettinger to secure the victory. The Capitals are 0-4 in shootouts this season. Thomas stopped 33 shots for the Bruins, who got first-period goals from Phil Kessel and Brad Stuart.
Boston outshot Washington 14-7 during a scoreless third period and 5-1 in overtime.
Dainius Zubrus scored his 12th goal and Pettinger had a short-handed tally for the Capitals, who trailed 2-0 in the game's 15th minute. Kolzig had 33 saves, and Alex Ovechkin and Alexander Semin each had an assist.
Washington had won two straight and four of five.