Jason Pominville scored midway through the first period, and Ryan Miller notched his second shutout in the series, which is tied at two games apiece. Game 5 is Friday night at the Wells Fargo Center.
When the final seconds disappeared, there were several scrums, and fans threw cups and bottles on the ice toward the Flyers.
Highlighting Miller's 32-save night - and his second 1-0 win in the series - was a sensational stop on ex-teammate Danny Briere with 8 minutes, 50 seconds left.
Briere, alone in front, made a series of dekes before Miller gloved his forehand shot from the goalmouth to preserve the 1-0 lead.
"You have to score on those chances," Briere said. "It was a good save by Ryan."
Briere said he may have had "too much time to think, and the fact that I was at a standstill" hurt him. "Usually we're used to coming in with speed, moving your legs and going one way or the other. But I couldn't really make a move because I had no speed. I just tried to make a quick move and get it up, but I couldn't really go around him. I had to try to get it through him. I wish I could have it again."
"I just wanted to get my glove as close to the play as I could," Miller said after the Flyers were blanked at least twice in a playoff series for just the fourth time in franchise history. It's the first time they have lost two 1-0 games in a playoff series.
"It wasn't so much the reaction as the anticipation that he was going to try to get it over me."
Carter, who had 36 goals in the regular season, left the game with 2:12 remaining in the first period, apparently suffering a knee injury. He did not return, and he was limping badly after the game.
General manager Paul Holmgren said afterward that Carter was day-to-day.
The loss may cause Chris Pronger to return to the ice in Game 5. Pronger has been sidelined for about five weeks as his surgically repaired right hand heals.
The Flyers masterfully killed the five-minute major to Richards that stretched into the third period.
Miller made a nice save on Kris Versteeg with 9:37 left, the one on Briere, and a clutch stick stop on Richards' rebound with 5:03 remaining, igniting bows and "Mil-ler" chants from the loud, sellout crowd.
Shortly before Miller reached his stick out to stop Richards, Brian Boucher stoned Tyler Ennis on a breakaway.
"We knew this wasn't going to be an easy series, but we worked hard all year and put ourselves in position to have home-ice advantage," Briere said. "Hopefully, we can use that to our advantage."
In the first 40 minutes, Miller was both very good (21 saves) and lucky (a second-period shot by Darroll Powe hit iron). He was tested the most by the blossoming James van Riemsdyk, who had six shots in the first two periods.
The Flyers' power play struggled again, going 0 for 3 and managing a total of four shots. Their power play is 2 for 21 in the series.
With just 2.8 seconds remaining in the second, Richards was given a five-minute penalty for elbowing Kaleta in the head, giving the Flyers an uphill battle as they tried to overcome as 1-0 deficit.
Richards said he was protecting himself from Kaleta. So did coach Peter Laviolette and the captain's teammates.
"I think he was protecting himself because you never know what Patrick Kaleta is capable of," winger Kris Versteeg said. "He's a dangerous player out there when it comes down to it. You never know if he's going to run you from behind, or he's going to hit you without the puck."
Defenseman Sean O'Donnell said the Sabres seemed to want to get into a street fight with the Flyers.
"Their two wins are 1-0, so we obviously know what they want to do and what we want to do," Versteeg said. "It's all about coming out and being ready for Game 5."
Before the game Briere, Mr. Postseason, thought the first 20 minutes would be the key.
"I'm sure they won't want to go back to Philly, down three to one," he said. "What's going to be important for us is to match that intensity, especially in first period because I expect them to come out strong."
They did. The Sabres came out hitting, and the Flyers were content to play a defensive style in the game's first six minutes. The Flyers got a power play 5:55 into the game, but they did little, although Ville Leino had an open net in front but couldn't control a bouncing puck.
Midway through the first period, the Sabres struck first as Pominville, who has had a quiet series, finished a tic-tac-toe passing play, tapping in a feed from Rob Niedermayer. Boucher had no chance.
About three minutes later, the Flyers had an abbreviated power play, and only a diving block by defenseman Tyler Myers prevented van Riemsdyk from scoring the equalizer as he fired at an open net with 7:18 left in the first.
Myers, who drove a shot off the post in the opening period, and Carter went to their respective locker rooms after colliding with 2:12 to go in the first. Myers returned for the second period.
Van Riemsdyk made a pair of dazzling moves to get around the Sabres' defense with 19 seconds left in the first, but he was thwarted by Miller.
Contact staff writer Sam Carchidi at firstname.lastname@example.org. Follow him on Twitter at www.twitter/BroadStBull.com