St Louis' Vladimir Sobotka pulled a score back in the second period but John Carlson wrapped it up later in the same period for the Capitals.
The Chicago Blackhawks bounced back from defeat by the Nashville Predators with a 5-1 victory over the San Jose Sharks.
Goalie Corey Crawford made 23 saves and Patrick Sharp had a three-point game (two goals).
The Columbus Blue Jackets began a five-game Canadian road trip with a 4-1 win over the Ottawa Senators.
Ryan Johansen, RJ Umberger, Fedor Tyutin and Derek MacKenzie scored for the Blue Jackets, Erik Karlsson replying for the Senators.
Minnesota Wild triumphed 2-1 over the Winnipeg Jets, the Dallas Stars edged the Vancouver Canucks by the same scoreline and the Los Angeles Kings took the honours by virtue of a 1-0 victory over the New York Rangers.