Dennis Wideman and Cody Eakin also scored as Washington claimed a second straight win going into the All-Star Game break.
The Caps got the victory despite the absence of captain Alex Ovechkin, who sat out the contest as part of three-game suspension.
The superstar forward announced before the contest he would sit out the All-Star Game.
Tomas Vokoun earned the victory with 29 saves.
Brad Marchand and Tyler Seguin scored for Boston, which absorbed its fourth setback in seven games.
Tuukka Rask made 18 saves for the Bruins.