Mark Streit, Wayne Simmonds and Matt Read also had goals for the Flyers.
Alex Ovechkin and Eric Fehr scored for Washington.
Two days after blowing a 4-1 third-period lead at Washington in a 5-4 shootout loss, the Flyers rallied to win their seventh consecutive home game.
Steve Mason made 24 saves for Philadelphia, which evened its record at 15-15-4. The Flyers are 12-6-4 since an embarrassing 7-0 loss at home to the Capitals on Nov. 1. They'll try to go over .500 for the first time this season Thursday night when they host Columbus.
Down 2-1, the Flyers stormed back with three straight goals, including a pair on the same power play in the second period.
First, Read scored his team-high 10th goal on a wrister to tie it at 2. Then Washington's Tom Wilson received a 5-minute major and ejection for charging. Wilson sent Brayden Schenn crashing headfirst into the boards with a hit from behind.
Schenn didn't return, but the Flyers made the most of their 5-minute man advantage.
Streit fired a one-timer from the left point past goalie Braden Holtby to make it 3-2. Voracek then slid one inside the near post 72 seconds later for a 4-2 lead.
Simmonds extended the lead to 5-2 in the third period, and this time the Flyers held onto a three-goal cushion.
After a scoreless first period, Ovechkin got the scoring started 40 seconds into the second on a power play. Nicklas Backstrom's pass from the far side of the net bounced off defenseman Nicklas Grossmann's skate, trickled away from Mason and went to Ovechkin, who backhanded it in for his NHL-best 28th goal.
The Flyers answered 58 seconds later when Voracek took a pass from Braydon Coburn and skated in with Claude Giroux on a 2-on-1 break. Voracek kept the puck and fired a wrister that beat Holtby to the stick side.
Fehr gave the Capitals a 2-1 lead in the second period when he scored on a one-timer off a perfect centering pass from behind the net by Troy Brouwer.
NOTES: The Capitals recalled C Casey Wellman from the AHL's Hershey Bears. Wellman had 13 points (seven goals, six assists) in 23 games. ... Voracek has five goals in the last five games. ... Washington had played to a shootout in its previous three games. ... Simmonds snapped a 10-game drought with the goal.