Washington began the night with a two-point lead over Winnipeg in the battle for the Southeast Division title. Carolina lost its seventh in a row in its continued slide out of the playoff race.
Jeff Skinner gave Carolina the lead 5:01 into the game, but Braden Holtby was perfect the rest of the way while stopping 43 shots.
Brouwer's first goal tied it 8:08 into the second and Mike Green scored less than 3 minutes later to put the Capitals in front. Brouwer tacked on an empty-net goal with 6 seconds to go in the third.
Justin Peters gave up two goals on 30 shots for the Hurricanes.