The Capitals scored twice in the opening period and wound up getting just 16 shots on goal for the entire game. Carey Price let three of them get by, however, and the Canadiens could not build on a 4-1 win over the New York Rangers last weekend.
Mathieu Perreault and Marcus Johansson delivered the first-period goals and Alex Ovechkin scored during a 4-minute power play in the second.
The shutout was the sixth of Neuvirth's career.
Montreal was unable to cash in on any of its seven power-play chances and has scored just once in its last 18 opportunities with the man advantage.