The Senators have bounced back from a five-game skid to win four in a row and they remained in sixth place in the Eastern Conference -- one point behind No. 5 Toronto.
Kyle Turris scored the first and last goals for the Senators, who dealt the Capitals a potentially damaging setback.
Turris scored just 1:15 into the game, but Mike Ribeiro tied it for Washington with 8:46 to go in the first period.
Cory Conacher put Ottawa back in front 2 minutes later and Anderson protected the 2-1 lead until Turris scored into an empty net with 1:27 to go in regulation.
Braden Holtby allowed two goals on 35 shots and Washington suffered its first loss in regulation since March 26.
Washington remained stuck on 50 points and is still out front in the Southeast Division -- the weakest in the NHL.
Winnipeg, however, moved within two points of the Capitals for the division lead by winning in overtime against Carolina. If Winnipeg winds up capturing the division title, Washington could find itself out of the playoffs.