The Bruins gained a point and moved into seventh place in the Eastern Conference with 85 points. Montreal is sixth with 86 points and Philadelphia is in eighth place with 84 points.
Laich's goal came 20 seconds after Boston's Dennis Wideman was called for high-sticking, and the Capitals had the four-on-three advantage.
Laich beat Boston goalie Tuukka Rask, who finished with 27 saves. It was Laich's 25th goal of the season. Alex Ovechkin finished with two assists.
The Capitals played their first game as winners of the Presidents' Trophy for most points in the league. They clinched home-ice advantage throughout the playoffs on Sunday night when San Jose lost in overtime to Colorado.
Nicklas Backstrom, who also assisted on the other two Washington goals, gave the Capitals a 1-0 lead at 7:36 of the first period with his 31st goal. Backstrom took a pass from Ovechkin and his slap shot trickled past Rask. The game was delayed for five minutes while the goal was being reviewed.
With 1.6 seconds left in the period, the Bruins tied the score at 1 when Wideman's shot from the left point beat a screened Jose Theodore. It was Wideman's fifth goal of the season.
Boston took a 2-1 lead when Patrice Bergeron took a pass from Milan Lucic and deked Theodore out of position and guided the puck into the net. The goal at 7:55 of the second period was Bergeron's 19th of the season.
Theodore stopped 28 shots.
Mike Knuble scored his 27th goal when he took a pass from Ovechkin and in a scramble, tapped it past Rask at 19:31 to tie the game at 2. This goal was also reviewed, but the call stood.
Boston will conclude the regular season on April 11 when it returns to Washington.
Notes
Washington coach Bruce Boudreau says that he won't announce his starting playoff goalie until just before the Capitals' first game. … Boston was without D Dennis Seidenberg. He cut his left wrist in Saturday's game against Toronto. He tried to practice on Monday morning, but was unable to finish. … The Bruins were also without LW Shawn Thornton (upper body), D Andrew Ference (hernia) and D Mark Stuart (left pinkie). C Trent Whitfield was a healthy scratch. … Boston D Adam McQuaid played for the first time since Feb. 13. He had been out with a concussion. … Washington D Mike Green was a healthy scratch.