The Flyers, who had few good scoring chances, have gone 316 minutes, 43 seconds without a post-season regulation goal, shattering the previous mark of 277:44 set by the Boston Bruins from 1933-35.
The last playoff goal not scored in overtime by Philadelphia came off the stick of defenseman Chris Therien at 3:17 of the third period of Game 5 of the 2001 conference quarterfinals against Buffalo.
"It's obviously frustrating, but I don't have an answer," Flyers center Adam Oates said. "Or sometimes that answer is there's a goaltender at the other end who can do no wrong. Tonight, moreso than any other, I thought he played his best and made some spectacular saves."
Patrick Lalime stopped 28 shots to become the fifth goaltender in post-season history and the second in as many nights to record three consecutive shutouts. St. Louis' Brent Johnson joined the elite club Tuesday night.
"It's a team effort," Lalime said. "Give credit to them, you cannot do it yourself. But the most important thing is the win."
"That's the best I've seen him play, and it rubs off on everybody," Ottawa defenseman Zdeno Chara said. "I think this is the best I've seen this team play all year."
Clint Benedict of the 1926 Montreal Maroons, John Ross Roach of the 1929 New York Rangers and Frank McCool of the 1945 Toronto Maple Leafs also had three straight post-season shutouts.
"I don't know about the shutouts, but I think we were confident in ourselves," Lalime said. "We knew we could do the job. It's not that we didn't play well in the past, we just didn't get the bounce on our side, things like that. Now we have a lot of confidence. We've got three in the bank, but we need the fourth one to win it."
"Patrick's playing with confidence and challenging the puck," Ottawa captain Daniel Alfredsson added. "And like all good goalies, he's getting some breaks right now."
Lalime, who lost his first five playoff decisions before reeling off this shutout streak, will have the chance to become the first goalie to register four shutouts in one playoff series on Friday night, when the teams return to Philadelphia for Game 5.
"It will be the toughest one," Lalime said. "I think the fourth one's always the toughest one to win. We've got to approach it that way, get in there and keep playing the same way."
"We know this is not over, but we'll try on Friday night to win the series," Chara said. "It's going to take a little bit of discipline but with some bite. We'll take the hits and give some of our own, and we'll be ready to face what they throw at us."
With time winding down in the first period, Alfredsson spotted Redden at the inside edge of the left faceoff circle. After receiving the pass, the second overall pick in the 1995 draft put the puck in the top left corner of the net with 20 seconds left to give the Senators a 1-0 lead.
"This feels really good," Alfredsson said. "I thought they came out hard in the first period, but that late goal was huge for us. And when that happens, you know things are going well."
"We started out very well," Philadelphia captain Keith Primeau said. "Both goaltenders made some great stops, but that goal late in the first period zapped our energy."
Redden's goal was the first of the series scored in the opening period.
Ottawa, which never had won three straight playoff games, struck twice in a 2:02 span of the second period to seal the Flyers' fate.
Standing behind the Philadelphia net, Shawn McEachern fed Salo high in the slot. The Finnish defenseman skated in and forced Roman Cechmanek to drop to the ice, then slid a backhander around the outstretched goalie at 6:06 for his second career postseason tally.
Hossa made it 3-0 at 8:08 by one-timing a pass from McEachern in the right circle for his second goal of the series.
Ottawa was held scoreless on eight power-play chances and is two for 20 in the series.