The Capitals' win came just three days after the Rangers beat Washington 3-2 in New York. Washington finished the preseason 4-2-0, while the Rangers dropped to 3-3-1.
Laich opened the scoring with a goal that included a spin move to get clear of New York's Alexandre Giroux, giving him a clear shot past Rangers goalie Henrik Lundqvist. Semin gave the Capitals a two-score lead with a goal through traffic after Brendan Morrison had a chance bounce off the post. Laich assisted on the play.
The Capitals scored twice more in the opening minutes of the second period. Brian Pothier's slap shot was deflected in by Bourque 2:59 into the period. Knuble put in a rebound of Mike Green's shot 91 seconds later to give Washington a 4-0 lead.
New York got on the board when Anisimov scored on a power play at 6:52 in the third period. Grachev added another when he brought the puck up the ice and fired a shot from the right circle with about 7 1/2 minutes left in the game, and Brashear scored New York's third goal of the period with four minutes to play.
The Rangers had just 11 shots in the first two periods, but 20 in the third. Lundqvist faced 24 shots over two periods before being replaced by Stephen Valiquette.
Washington opens the regular season Thursday night at Boston. New York starts its campaign Friday at Pittsburgh.
Copyright by STATS LLC and The Associated Press
Arena: Verizon Center Location: Washington, District of Columbia
Attendance: 18,277 (99.3% full)
Brooks Laich Unassisted
Alexander Semin Assist: Tyler Sloan, Brooks Laich
Chris Bourque Assist: Brian Pothier, David Steckel
Mike Knuble Assist: Mike Green, Jeff Schultz
Artem Anisimov (power play) Assist: Michal Rozsival, Wade Redden