Anderson has won both of his starts since he signed a four-year, $12.75 million contract extension Monday. He stopped 29 shots in a 2-1 shootout win over the Rangers in New York on Thursday night.
Greening opened the scoring 13:25 into the second. Condra made it a two-goal lead with his fifth goal early in the third.
Semyon Varlamov stopped 21 shots for Washington, which played its second straight game without injured captain Alexander Ovechkin.
The Capitals, first in the Southeast Division with 96 points, won in Philadelphia on Tuesday night for their 11th victory in 12 games. They remain two points behind the Flyers for the Eastern Conference lead.
Ovechkin, who leads the Capitals with 77 points, was shut down Monday for seven to 10 days with an undisclosed injury.
Washington was shut out for the 10th time this season.
Anderson made a sprawling save early in the second to keep the game scoreless. He stopped Brooks Laich's backhand right after he denied Alexander Semin on a partial breakaway after the Washington right wing came out of the penalty box.
Ottawa, which is last overall in the East, took a 1-0 lead when Greening got credit for his fourth goal on a play that required a lengthy video review.
The rookie center was in the crease and fell forward into the crossbar, coming into contact with Varlamov while the puck crossed the line. The on-ice ruling of a goal was upheld, to the displeasure of Capitals coach Bruce Boudreau.
Condra scored 2:12 into the third. Milan Michalek cut off Varlamov's clearing attempt in the right corner and fed a pass to Condra, who snapped a shot past Varlamov.
Senators defenseman Patrick Weincioch lay on the ice against the boards behind the Ottawa net briefly after he was checked by Washington's Matt Bradley. Weincioch remained in the game.
Zack Smith got an instigating minor, fighting major and 10-minute misconduct when he came to his teammate's defense, bloodying Bradley, who was given a boarding minor and fighting major, in the ensuing scrap.
NOTES: Capitals LW D.J. King fought Ottawa's Francis Lessard 2:53 in. ... Michalek returned after missing 12 games with a broken foot.