Anderson, acquired Feb. 18 from Colorado, has won both of his starts since he signed a four-year contract extension Monday. He stopped 29 shots in a 2-1 shootout win against the Rangers in New York on Thursday night.
"He was good," Capitals coach Bruce Boudreau said. "There's a reason they gave him four years. They knew a good goalie when they saw one."
Greening opened the scoring 13:25 into the second period, and Condra added his fifth goal early in the third. Anderson did the rest.
"I think for me it's just a matter of keeping the team in the game, giving them an opportunity to stay in the game and win it," Anderson said. "It's one of those nights where it's going to be a lucky bounce for us to win, or for them to win, and that's kind of the way it played out."
Semyon Varlamov, returning from a knee injury, stopped 21 shots for Washington, which played its second straight game without injured captain Alex Ovechkin -- he's out with an undisclosed injury and won't be back until next week at the earliest. The Caps finish a six-game road trip in Montreal on Saturday.
The Capitals, first in the Southeast Division with 96 points, lost for only the second time in 13 games. They remained two points behind the Flyers for the Eastern Conference lead, but were 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 backhander right after he denied Alexander Semin on a partial breakaway after the Washington forward came out of the penalty box.
Ottawa took a 1-0 lead when Greening got credit for his fourth goal on a play that required a lengthy video review.
"I felt like it was a goal but I have to say that as time went by and I was on the bench, I was thinking, 'Wow! Why is this taking so much time?" Greening said.
Greening 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, much to the displeasure of Boudreau.
"I wanted to know whether he was interfered with and I think the question in Toronto was whether he kicked it in," Boudreau said.
Condra scored 2:12 into the third. Milan Michalek cut off Varlamov's clearing attempt in the right corner and fed Condra, who snapped a shot past Varlamov.
The Senators are officially eliminated from the playoff hunt, but they've moved within a point of passing Florida for 14th place and it's important to Ottawa coach Cory Clouston for his team to finish the season strong.
"Since the (trade deadline) changes were made, I think we're 12-6-1," said Clouston. "We've got good goaltending, good effort most nights and good structure to our game.
"We've got young guys coming up, assuming big roles and taking advantage of the opportunity and they're learning as they've gone on."
Material from team media and wire services was used in this report