Kostitsyn had a penalty just a few minutes earlier that helped Washington tie the score.
Sergei Kostitsyn and brother Andrei each had a goal and an assist and Tomas Plekanec scored twice while the Canadiens matched their longest winning streak in nearly three months with a fourth straight victory.
Robert Lang started the scoring in the third-period, which also saw Washington score twice, and Jaroslav Halak held off the Capitals down the stretch to earn the victory with 31 saves. Halak has started the last five games for Montreal while No. 1 goaltender Carey Price recovers from a lower-body injury.
Alexander Semin scored two goals and Michael Nylander had a goal and an assist for Washington. Brent Johnson allowed five goals on 35 shots in the loss.