Bryzgalov made 29 saves, none bigger than two on Vanek in the final 15 seconds.
"I just tried to stop the puck," Brzygalov said with a shrug. "Everybody battled hard, and we were rewarded with two points."
Bryzgalov's strong play and an early, three-goal onslaught - started by rookie center Sean Couturier - carried the Flyers to their second straight win.
Used primarily as a defensive specialist in the season's first month, Couturier was moved to the second line because of injuries to Danny Briere and Matt Read - and it took the unassuming 18-year-old less than two minutes to make the most of the promotion.
Couturier scored on a rebound 1 minute, 43 seconds into the game, beginning a three-goal flurry in the first 6:23. Only 15 times in franchise history have the Flyers scored three faster goals. The quickest three goals were scored in 2:19 in a 6-4 win over Atlanta in 2001.
Bryzgalov had his second consecutive strong game, outplaying the heralded Ryan Miller, who was pulled after the early onslaught and replaced by Jhonas Enroth. It was the third-quickest exit in Miller's brilliant career.
The Sabres got a gift goal with 11:31 left to get within 3-2. Rookie Luke Adam, from behind the net, threw a pass out front that deflected off defenseman Kimmo Timonen's skate and through Bryzgalov's legs.
The Flyers returned to the arena where they scored a Game 6 overtime victory - thanks to a goal by Ville Leino - en route to winning the first-round playoff series in seven games last spring.
Leino signed a six-year, $27 million contract with the Sabres in the offseason and, thus far, has been a free-agent bust. He entered the night with one goal and one assist in 10 games.
In an effort to get Leino jump-started, Sabres coach Lindy Ruff began the night with the former Flyer on the first line, between high-scoring wingers Jason Pominville and Vanek, for the first time this season.
Leino, facing a team that used just eight players Wednesday that opposed Buffalo in last season's playoffs, was soon demoted to a lesser line as the Flyers jumped out to their quick lead. Couturier's goal was followed by scores from James van Riemsdyk and Scott Hartnell
Couturier and van Riemsdyk scored 13 seconds apart.
Hartnell chased Miller on a blast from the top of the left circle, giving the winger 10 points (five goals, five assists) in his last five games.
"That first five minutes was some of the best hockey we've played so far," Hartnell said. "We were fast, we were hitting, we were getting loose pucks."
Hartnell's goal finished a three on two with Claude Giroux and Jaromir Jagr.
Buffalo got to within 3-1 with 12:11 left in the second period when Andrej Sekera scored off a carom off the backboards.
Bryzgalov made several key saves during a second period in which the Sabres outshot the Flyers, 15-5.
The Flyers' early 3-0 lead "was like a football game when you're up, 21-0, and there are no guarantees you're going to win," Jagr said. "You have to somehow finish the game, and it's not easy. You don't want to open it up, but you don't want to play it safe."
Because of injuries, the Flyers juggled three of their four lines; only the top line, with Giroux centering Hartnell and Jagr, remained intact.
Couturier centered van Riemsdyk and Jakub Voracek on the second line, while Max Talbot centered Wayne Simmonds and Andreas Nodl on the third line. Ben Holmstrom, recalled from the Phantoms on Tuesday, centered Zac Rinaldo and Jody Shelley on the fourth line.
Contact staff writer Sam Carchidi at firstname.lastname@example.org or @BroadStBull on Twitter.