Erik Cole had a goal and three assists, as he and Brind'Amour formed a two-man attack for the Hurricanes -- who beat the Capitals, 5-0, Nov. 9, and have won four times in their last five games.
The Hurricanes led, 2-0, at the second intermission, and never trailed.
Carolina goalie John Grahame was beaten once on 22 Washington shots.
Richard Zednik scored a power-play goal at 9:28 of the third period after assists by Ben Clymer and Kris Beech. Goaltender Olaf Kolzig gave up four goals on 29 shots in Washington's second straight loss.
On the power play, the Hurricanes scored twice in six chances, and the Capitals went 1-for-5.