Maxime Talbot, Matt Read and Claude Giroux also scored for the Flyers, who moved within two points of the idle New York Rangers and New York Islanders for the final playoff spot in the Eastern Conference.
The Capitals are a point ahead of Philadelphia in a jumbled East.
``Thirteen games left is a lot of games,'' Voracek said. ``We haven't been on a hot streak yet. Maybe we'll start one now.''
Desperate to get a point, the Flyers tied it at 4 when Timonen ripped a slap shot past Braden Holtby after several chances in front. Timonen lifted his arms in the air and pointed toward the sky in celebration.
Timonen then set up Fedotenko with a perfect crossing pass in OT to cap off a remarkable comeback and set off a wild celebration.
``He saw an opportunity to give it right back to me and it was an easy backdoor tap-in,'' Fedotenko said. ``It's a great feeling.''
The Flyers have won two in a row and are trying to avoid missing the playoffs for the first time since 2007 and second in 18 years.
The Capitals took advantage of a four-minute power play in the third period after Voracek pounded Steve Olesky with a barrage of rights and left him with a bloody face. Voracek went after Olesky after his hard check on Giroux. He got two minutes for instigating and two minutes for fighting with a visor.
``I'm proud of him,'' Timonen said. ``You don't hit guys like Giroux like that and not pay the price.''
Voracek hadn't fought all season and said he wasn't aware of the visor rule.
A minute into the man-advantage, Johansson took advantage of a turnover and fired a shot from inside the left circle past Ilya Bryzgalov to give the Capitals a 3-2 lead.
Then, Ovechkin ripped a slap shot from above the left faceoff circle past Bryzgalov for his eighth goal in eight games to make it 4-2.
But the Flyers rallied.
``We needed to make more of an effort on our part the last couple of minutes there,'' Backstrom said.
Giroux got the Flyers within one on a power-play goal with 7:12 left.
Washington tied it at 2 late in the second period right after denying the Flyers on a power play. Green came out of the penalty box, took an outlet pass from Brooks Laich and beat Bryzgalov on the breakaway.
``We got a point there, but we obviously want two there,'' Capitals coach Adam Oates said. ``We let it get away.''
The Flyers didn't register their first shot on Holtby until midway through the first. Seconds later, Talbot shot one between Holtby's legs to tie it at 1.
Read took a long pass from Giroux, broke in alone on Holtby and ripped it past him to give Philadelphia a 2-1 lead late in the first.
Shortly afterward, the Flyers had a goal negated because of a goaltender interference penalty on Wayne Simmonds. Giroux was called for a face-off violation before the puck dropped, giving the Capitals a 5-on-3 advantage for two minutes.
But Bryzgalov made an outstanding left-to-right sliding save on Troy Brouwer's stuffer in front and Philadelphia killed it off.
Backstrom deflected Jack Hillen's slap shot past Bryzgalov to give the Capitals a 1-0 lead 4:29 into the first. It was Hillen's first point since an assist on Jan. 1, 2012.
NOTES: D Kent Huskins made his Flyers debut after coming over in a trade with Detroit on Saturday. ... Backstrom has 398 career points in 400 NHL games. No active player has more points in fewer games. ... Timonen's assist on Talbot's goal was his first point in eight games. ... The Capitals are 4-1-4 in their last nine games in Philadelphia. ... The Flyers had scored on five consecutive power-play chances before failing on their first opportunity in the first period.
Follow Rob Maaddi on Twitter: https://twitter.com/RobMaaddi