Brooks Laich and Mathieu Perreault provided the goals for the Capitals, who notched their third consecutive win to move four points ahead of both Winnipeg and Buffalo for the eighth and final playoff spot in the Eastern Conference.
Washington remains one point behind first-place Florida in the Southeast.
Jonas Gustavsson stopped 21 shots for Toronto team that was blanked for the second day in a row. The Maple Leafs, coming off a 1-0 shootout loss to Philadelphia on Saturday, have dropped four straight and 14 of 16 overall.
Washington failed to cash in a power play early in the contest, but Laich opened the scoring with a short-handed goal. Laich picked off a drop pass from Toronto rookie defenseman Jake Gardiner in the neutral zone and beat Gustavsson from the right circle with a wrister midway through the first period.
Perreault flipped a rebound off an Alexander Semin shot over a prone goalie from the side of the net to double the Capitals' advantage 42 seconds into the third period.
Neuvirth played in his 100th NHL game and recorded his seventh career shutout...Semin has 398 career points...The Capitals improved to 5-0-1 at home against Toronto since a 2-1 regulation defeat March 5, 2009...The Maple Leafs opened a five-game road trip.