The Flyers are 2-3 in shootouts this season and 26-46 in franchise history.
The Flyers outshot the Oilers, 38-16. Bryzgalov made 35 saves.
“He’s the reason we got a point tonight,” Edmonton center Jordan Eberle said.
Scott Hartnell's tip-in tied the score at 3 with 5 minutes, 32 seconds left, and it was the Flyers' first five-on-three goal this season. It was their third power-play goal in the game.
Bryzgalov flipped his stick in the air after Hartnell’s goal.
“I tried to lose the steam,” said Bryzgalov about the angry moment. “It was a little bit of frustration.”
About three minutes earlier, Edmonton had taken a 3-2 lead as David Perron's pass deflected off defenseman Nick Grossmann and past Steve Mason while the Oilers were on a power play.
Mason stopped Perron on a breakaway with 2:13 remaining in regulation.
Edmonton is now 3-22-2 against teams with a winning points percentage.
Wayne Simmonds scored a pair of second-period goals - both on the power play - as the Flyers overcame a 2-0 deficit and tied the game at 2.
Simmonds has scored two goals in each of his last three games.
In franchise history, a Flyer has scored multiple goals in three consecutive games three other times; the last had been by Reggie Leach in 1981. (In 1976, Leach and Ross Lonsberry did it.)
Simmonds tipped in Giroux's left-circle one-timer for the first goal, then finished off a slick tic-tac-toe play with Jake Voracek and Scott Hartnell with 7:47 left in the second.
Voracek extended his points streak to nine games, while Giroux increased his to eight games.
Mason robbed Justin Schultz out front with about two minutes left in the second, keeping the game tied.
The Oilers hit the crossbar and post on two shots in the first seven minutes of the third period.
Mistakes by defensemen Braydon Coburn and Mark Streit helped the Oilers take a 2-0 lead in the game's opening 4:02. It marked the first time this season the Flyers had allowed more than one goal in the opening period.
A Coburn turnover enabled Taylor Hall to go in alone, and he fired a shot that caromed off the inside of the left post and into the net, giving Edmonton a 1-0 lead after 28 seconds.
About 31/2 minutes later, Ryan Nugent-Hopkins made a tricky move to turn Streit inside out and then beat Mason with a shot from the high slot.
The Flyers bought out the remaining seven years of Bryzgalov's contract in the offseason, and he was facing his ex-teammates for the first time since he signed a free-agent contract last month with Edmonton.
"Any time a goalie switches teams, he's going to want to prove something to his old team," said Simmonds, who has a team-high 12 goals. "We knew he was going to bring his `A' game tonight."
The Flyers ended a five-game road losing streak, thanks mainly to a power play that was 3 for 5.
“I know them well, and they have many options on the power play, and it’s tough to defend,” said Bryzgalov, who was 4-7 in shootouts during his time with the Flyers.
Edmonton, which began the night with the 29th-best record in the 30-team league, was coming off a 2-0 win the previous night in Calgary.
The Flyers were playing their first game since Monday's 4-1 victory over Minnesota, their ninth straight home win.