Boston (64-12-5), which has won seven in a row, has 133 points, one more than the 1976-77 Montreal Canadiens (60-8 with 12 ties).
"The Montreal team that we surpassed only played 80 games. I think the [63] wins in 80 games is a little more significant, but it's a good year," Bruins coach Jim Montgomery said. "I care more that we're playing the right way."
Brad Marchand had a goal and two assists, Tomas Nosek had a goal and an assist, and David Pastrnak had two assists for the Bruins.
"If we don't go all the way, [the record] means nothing," Nosek said. "I will recognize it more as time goes on, [but] not right now."
Linus Ullmark made 19 saves for his 40th win of the season but left midway through the third period after colliding with his right post. Jeremy Swayman made six saves in relief.
"It was just a precaution," Montgomery said. "… Just some muscle tightening, that's all."
Tom Wilson and Nick Jensen scored for Washington (35-37-9), which has lost seven of its past eight games (1-6-1). Charlie Lindgren made 33 saves but also left early in the third period with an undisclosed injury after making an acrobatic save. Darcy Kuemper allowed one goal on seven shots in relief.
"[Lindgren] was amazing tonight," Jensen said. "There [were] definitely a few times that, me personally, I'm sure other people felt, we could help him out a little more, but he kept us in that game huge, and it was tough to see him go down like that with how well he was playing."