Anderson made 28 saves for the Capitals (35-15-5), who were coming off a 4-2 loss to the Flyers on Friday but have won three of their past four games.
"There was just so many encouraging things to see today, and it wasn't easy for us," Eller said. "We were down most of the game and killing off penalties late in the third. We weren't given anything today. We really had to work for it, and I think that makes it feel so much sweeter for all of us. It's a good feeling in our room right now."
The Pittsburgh Penguins clinched first place in the East on Saturday. The Boston Bruins and New York Islanders have the other Stanley Cup Playoff berths from the eight-team division.
Scott Laughton scored for the Flyers (24-23-8), who have lost five of seven. Lyon made 38 saves.
"It's disappointing that we were close to winning this game," Philadelphia coach Alain Vigneault said, "and it would have been real good for Alex to get another win here tonight, but unfortunately we weren't able to get the job done."
Washington went 6-2-0 against Philadelphia this season.
It was Anderson's second start of the season and first since a 4-3 win against the New Jersey Devils on Feb. 21.
"I thought he was really good. I thought he gave us a chance to win," Capitals coach Peter Laviolette said. "He made big saves. Looked really confident in there. Handled the puck really well."
Laughton entered the zone 2-on-1 with Nicolas Aube-Kubel, kept the puck, and scored with a high wrist shot from the right circle at 3:42 of the third period.
"Not many chances both ways," Laughton said. "They had a couple of good looks, and Al made some good saves, but kind of a neutral-zone game where you're kind of chasing around. But I thought we played well enough to try to squeak one out, but unfortunately not."