Kimmo Timonen, who contributed mightily to a key five-on-three penalty kill in the third period, iced the win with an empty-net goal with 17.8 seconds left.
Zherdev has had a different outlook since no one claimed him off waivers.
"Since that time, what's been most impressive to me is his attitude," coach Peter Laviolette said. "He's worked really hard, and he's committed just like everybody else. He got an opportunity tonight and scored a big goal for us.
"There's always two different roads you can go down at that point," Laviolette said, referring to the waiver situation. "You can go south and maybe never get a player back, or you can do what you have to do, and he's worked really hard with the coaches and very hard with [trainer] Jimmy McCrossin to keep himself in shape."
Game 4 is Wednesday in Buffalo.
With 13 minutes, 1 second left, Buffalo had a five-on-three power play for 1:15, but the Flyers killed it off skillfully, allowing just one shot in that span. Defensemen Timonen (plus-three) and Braydon Coburn (plus-three), and center Mike Richards did the bulk of the work on the two-man disadvantage.
"That," said Boucher, whose team got a breather when he needed a mask repair during the penalty kill, "was the pivotal part of the game."
In the franchise's history, the Flyers are 18-3 when they have a 2-1 lead in a series.
Ex-Sabre Danny Briere, a certified Buffalo killer, gave the Flyers a 2-1 lead by converting a Scott Hartnell pass with 17:36 left in the second period.
Hartnell pressured defenseman Chris Butler into overskating the puck behind the net. Hartnell then found Briere, who has five goals and four assists in seven games in Buffalo since he became a Flyer.
Zherdev increased the lead to 3-1 with 3:16 remaining in the second after a slick feed from Richards. Standing on the doorstep to the right of the goal, the winger tapped the pass into the net to give the Flyers a brief two-goal lead.
"Right now, I'm just focusing on the playoffs and working hard," said Zherdev.
Briere knows how Zherdev felt when he was put on waivers. He, too, was placed on waivers early in his career in Phoenix.
"That certainly was a wake-up call for me," Briere said. "All of a sudden, you realize nobody wants you. Before that, you're kind of blaming it on the coaching staff that you're not playing me; it's everybody else's fault, and then when you clear waivers and realize nobody wants you, you start to realize that the problem is yourself.
"To his credit, he went back and has been working hard, off the ice as well," Briere added. "He's been . . . staying in shape and waiting for his chance. I think everyone is happy for him to score a big goal like that."
About 11/2 minutes after Zherdev's first career playoff goal, Nathan Gerbe scored from the left circle after Boucher gave him a long, juicy rebound. That brought the Sabres to within 3-2 and reenergized the crowd.
The Flyers controlled the first part of the opening period, getting a power-play goal from Jeff Carter and allowing Buffalo only three shots in the first nine minutes. (The Sabres lost agitator Patrick Kaleta to an unspecified injury early in the game.)
Carter, who had just two goals in his previous 10 games, scored from the right circle with 15:18 left in the first period. The shot appeared to deflect off defenseman Mike Weber and past startled goalie Ryan Miller.
"It was kind of a broken play," said Carter, who finished with nine shots, including four on net. "We just tried to dump it in and it hit their D. It gave me some room to walk in for an open shot, and I was lucky to get one through."
About seven minutes later, Drew Stafford scored the equalizer - firing a shot from the high slot - while Buffalo was on a power play because of Coburn's interference penalty.
That triggered mocking chants of Boo-SHAY, Boo-SHAY from the fired-up sellout crowd.
As much as the Flyers controlled the first half of the first period, Buffalo dominated the second half of the session and finished with a 16-6 shots advantage in the first 20 minutes.
Along with the five-on-three, the Flyers killed a double-minor to Hartnell that carried into the second period. Those kills loomed large.
"The penalty killers didn't give up a whole lot of opportunities," Laviolette said.
Contact staff writer Sam Carchidi at email@example.com. Follow on Twiotter at www.twitter.com/BroadStBull.