Bryzgalov made two shootout saves, and another shot hit the post.
In the last four games, Bryzgalov (29 saves) has stopped 128 of 130 shots, a stunning .985 save percentage.
"He's unreal. He's battling really hard right now, and he's winning us games," said defenseman Andreas Lilja, who blocked seven shots. "It's fun. It's easy with the way Bryz is playing."
Defenseman Nick Grossmann (eight hits, five blocked shots) and winger Scott Hartnell (seven hits) also played key roles in Bryzgalov's fifth shutout.
With 3 minutes, 29 seconds left in overtime, Bryzgalov stoned Phil Kessel (again) on a breakaway.
"He's smart playing the puck, and when shots get through, he's covering up rebounds and hardly giving any second chances," Hartnell said. "And the D are playing great in front of him. It's a deadly combination to have."
Bryzgalov, who praised his defensemen and forwards, politely refused to elaborate about his hot streak.
"I don't want to talk about me," Bryzgalov said. "We're playing a team game. It's a team sport and let's talk about the team."
The Maple Leafs, fighting for their playoff lives, had the game stolen by Bryzgalov.
"Their chances were a lot more than ours and they were better than ours," coach Peter Laviolette said. "He made the saves at the right time. He's been sharp and tonight was no different - and we needed him to be."
Bryzgalov made a handful of difficult saves in the second period, enabling the Flyers to head into the final 20 minutes in a scoreless tie. Bryzgalov, who had a 1.95 goals-against average and .926 save percentage in his previous 11 games, robbed Matt Frattin on a one-timer from the slot with 4:55 to go in the second. He made the save just as a Flyers penalty expired.
With 1:26 left in the second, Bryzgalov denied John-Michael Liles on Toronto's only shot in three power-play chances in the first two periods. The Flyers outshot the Leafs, 2-1, during those six shorthanded minutes.
The Flyers' offense was flat in the first 40 minutes, and several second-period line changes by Laviolette - and Wayne Simmonds' one-sided win over Joey Crabb in a fight - didn't ignite things.
In one of the moves, Laviolette shifted Jaromir Jagr back with Giroux and Hartnell at the start of the second period. Jagr, getting back to form after suffering a hip injury Tuesday against Detroit, had started the night on a line with Jody Shelley and Eric Wellwood.
Toronto's David Steckel, alone in front, knocked a shot off the post with 12:05 left in the first, and Bryzgalov made a nice glove save on Kessel with 3:05 to go in the period.
With a little over two minutes left in the first, Giroux had the Flyers' best early opportunity, but he fired high and wide on a breakaway.
Giroux set up Max Talbot in front for a shorthanded chance late in the second period, but Jonas Gutavsson made one of his best saves of the night.
Forty-three seconds into the third period, Toronto's Clarke MacArthur missed an open net as he was alone in front. After a stoppage, MacArthur had a pained expression as he shook his head and grabbed his helmet.
The Flyers won despite not having a power play. They stopped all three of the Leafs' power plays. It was the first time the Flyers did not have a PP since 2008.
Contact Sam Carchidi at firstname.lastname@example.org or on Twitter @BroadStBull.