Ovechkin's two early scores were both assisted by Nicklas Backstrom and Mikhail Grabovsky added another goal before the period was out, staking the Capitals to a big early lead.
John Carlson added a power-play goal for Washington, which began a three-game homestand with a third consecutive win.
Braden Holtby stopped 46-of-47 shots to secure the victory.
Vladimir Sobotka for the Blues, who were handed just their third regulation loss of the season.
Jaroslav Halak started in goal but was lifted in the first period after yielding three goals on six shots.
Brian Elliott relieved and turned aside 13-of-14 shots the rest of the way.