Chris Clark scored a short-handed goal with 2:57 left in the second period to complete his second career hat trick and give the Capitals a 3-0 lead. But the Bruins tied it, thanks to three assists from Marc Savard and a pair of power-play goals 65 seconds apart in the third after Washington spotted them a 5-on-3 advantage.
It stayed that way until the first three skaters missed in the shootout. Bergeron went between Kolzig's legs and Alex Ovechkin scored on a backhand before Phil Kessel clinched it.
Kolzig returned after missing 13 games with a knee injury. The Capitals were 1-8-4 without him.