Rookie Matt Read scored the game-winner in the shootout, and Bryzgalov - who redeemed himself - stopped four of five shootout shots.
Claude Giroux also scored in the shootout as the Flyers stunned the sellout crowd, winning for just the second time in seven shootouts this season.
Scott Hartnell, who scored his 29th and 30th goals, tied it at 3-3 while the Flyers were on a 5-on-3 power play with 12:25 left in regulation.
A little over three minutes later, Alex Tanguay scored on a penalty shot to put the Flames ahead, 4-3.
Tanguay went in on a breakaway and was lightly slashed by Pavel Kubina and was never pulled down. Incredibly, Tanguay was awarded a penalty shot, and he cashed in.
But the Flyers didn't quit.
With 7:39 to go, recently acquired defenseman Nick Grossman shot a wrister from the point which went off Hartnell, who set a screen in front. Hartnell, who scored two goals, tied the score at 4-4.
Earlier, Jakub Voracek won a board battle, went in alone and beat goalie Miikka Kiprusoff with 4:13 left in the second period, getting the Flyers within 3-1. With 33.9 seconds left in the period, Kiprusoff stopped Braydon Coburn's point drive, but the rebound bounced off Calgary defenseman Scott Hannan and into the net, getting the Flyers to within 3-2.
Voracek's goal ended the Flyers scoreless drought at 95:47.
The Flyers, who nearly won it at the end of overtime as Andrej Meszaros fired wide in the closing seconds, had a 45-21 shots advantage after regulation.
After having surrendered the first goal in each of the previous six games, the Flyers preached the importance of making their opponent play from behind for a change.
Bryzgalov, who is starting to resemble Dick "Dr. Strangeglove" Stuart - the former Phillies first baseman with a penchant for defensive miscues - failed to glove defenseman Mark Giordano's point drive. Make that seven straight games in which the Flyers' opponent scored first.
Giordano's power-play goal, scored after defenseman Braydon Coburn failed to clear the puck, gave Calgary a 1-0 lead after just 3:45.
It was the fifth power-play goal the Flyers yielded out of the last six times they were shorthanded.
About 1½ minutes later, Matt Stajan scored as he partially fanned from the high slot - CBC Television clocked his "change-up" at 41 m.p.h. - to make it 2-0.
The Flyers' mission was to keep their focus for 60 minutes, something they neglected to do in their previous game - a 2-0 loss in Edmonton on Thursday.
In that game, the Flyers played a listless second period, getting outscored, 2-0, and outshot, 15-6. Against the second-worst team in the NHL.
"Disgraceful," Flyers coach Peter Laviolette called the second period.
With just 21 games left in the regular season, the Flyers need to start showing urgency, start solidifying their position in the tight Eastern Conference.
"We need to be playing our best hockey going into the playoffs," Hartnell said before the game.
The Flyers controlled most of the first period, outshooting Calgary, 15-6 - though they had only a handful of good scoring chances.
Flames goalie Kiprusoff had all the answers. Bryzgalov didn't.
Calgary took a 3-0 lead on a shorthanded goal by Tom Kostopoulos with 7:05 left in the stanza.
Contact staff writer Sam Carchidi at email@example.com or @BroadStBull on Twitter.