Tom Wilson had a goal and an assist, and Evgeny Kuznetsov and Dylan Strome each had two assists for the Capitals. Darcy Kuemper made 16 saves.
Milan Lucic had a goal and an assist, and Linus Ullmark made 36 saves for the Bruins.
Connor McMichael scored 26 seconds into the first period to give Washington a 1-0 lead.
James van Riemsdyk scored 27 seconds later at :53 to tie it 1-1, and Mason Lohrei put Boston in front 2-1 at 2:42.
Wilson responded with a power-play goal to tie it 2-2 at 7:51 before Sonny Milano gave the Capitals a 3-2 lead at 15:57.
Lucic tied it 3-3 at 8:23 of the second period.
Carlson put Washington back in front 4-3 with a power-play goal 43 seconds into the third period, but Matthew Poitras tied it 4-4 at 4:57.
