Brouwer's power-play tally 5 minutes into the second period broke a 1-1 tie and triggered big middle frame for the Capitals, who scored three times during the span to grab control of the game.
Mathieu Perreault and Marcus Johansson also provided and a goal and an assist each as Washington logged just its second win in six games. Alex Ovechkin and Jason Chimera scored and Braden Holtby turned aside 27 shots for the Capitals.
Buffalo got two goals from Cory Hodgson but couldn't avoid its sixth defeat in seven games.
Ryan Miller made 20 saves for the Sabres.