Garnet Hathaway scored two goals for the Capitals, who are the No. 2 seed. Craig Anderson made 44 saves.
Game 3 will be played at Boston on Wednesday (6:30 p.m. ET; NBCSN, SN360, SNE, SNO, SNP, TVAS, NESN, NBCSWA).
"We knew they were going to come back with a little bit more bite tonight offensively, and some of the things we shot ourselves in the foot a little bit with execution," Washington coach Peter Laviolette said. "So there's things I think we can do better as we head to Boston."
Anderson, who turns 40 on Friday, made his first start in the Stanley Cup Playoffs since a 3-2 loss in double overtime with the Ottawa Senators in Game 7 of the 2017 Eastern Conference Final against the Pittsburgh Penguins. He made 21 saves in relief in a 3-2 overtime win in Game 1 on Saturday after Vitek Vanecek sustained a lower-body injury in the first period.
"We needed him to play great, and I thought he did," Hathaway said of Anderson. "It's tough, you know, last minute, couple minutes left for a goal to tie it and then [it ends] quick in overtime. I think it kind of overshadows how we played and how he played especially."