T.J. Oshie scored his fourth goal in two games for the Capitals (34-15-5), who have lost three of their past five games. Vitek Vanecek made 25 saves.
Washington trails the Pittsburgh Penguins by two points for first in the MassMutual East Division with one game in hand. The Capitals, Penguins, Boston Bruins and New York Islanders have clinched the four Stanley Cup Playoff berths from the division.
"These are big points for us that we let get by here, so there can't be any excuses," Washington coach Peter Laviolette said. "I just thought we were on our heels too much. They had some good pace in the first period, and we were reacting to them. We were turning pucks over because we weren't on our toes, we weren't sharp."
Rookie Wade Allison scored twice in the second period for his first multigoal game in the NHL for the Flyers (24-23-7), who won for the second time in six games. Brian Elliott made 28 saves.
"There's no doubt that guys have been very positive and very good with the young players brought in here lately, and tonight I thought our whole group skated well," Philadelphia coach Alain Vigneault said. "I like the energy we brought to the table and I hope we can do the same thing tomorrow."
The teams will conclude their season series here Saturday. The Capitals are 5-2-0 against the Flyers. They had won five in a row.
Joel Farabee tucked in a loose puck from the right of the net to give Philadelphia a 1-0 lead at 1:44 of the first period.
Daniel Sprong tied it 1-1 at 16:19. He scored his sixth goal in six games with a wrist shot from the slot off Anthony Mantha's pass from behind the net.
"I think there were times in the game where we were the better team and there were times where we took our foot off the gas and they had their chances," Sprong said.