After posting a 33-save shutout in Game Two to even the series, Cechmanek was shaky in this one, allowing two goals on 20 shots, including the tying tally on a wraparound.
But once the overtime began, Cechmanek was stellar, denying two breakaway attempts among his six saves.
Stationed along the left boards, Redden wristed a shot toward the net. With defenseman Dmitry Yushkevich and Vaclav Varada standing in front of him, Cechmanek had no chance to keep the puck from going between him and the left goalpost.
"We got the puck in there," Redden said. "Varada did a good job on the forecheck. The puck came around on the boards to my side. I just tried to get it at the net. There was some traffic in front of the net and it found its way in. ... That goal wasn't a pretty one by any means, but we'll take those."
"It went through four or five players, including their guy," Philadelphia coach Ken Hitchcock said. "A seeing-eye dog. Unbelievable. It went under an arm, between a stick and a body and in on the short side."
Redden's sixth career postseason goal gave Ottawa its first playoff victory in 23 tries when trailing after two periods.
John LeClair and Sami Kapanen tallied for the Flyers, who have scored first in each game of the series.
Game Four is Thursday in Philadelphia.
After a close-checking affair in Game Two, things were wide open from the start Tuesday.
Kapanen nearly gave the Flyers the lead 2 1/2 minutes into the game, but Patrick Lalime turned aside his shot from alone in front. Just 70 seconds later, Alfredsson pounced on a turnover in the neutral zone and fired a wrist shot from just above the left faceoff circle that bounced off the left post.
Philadelphia broke through at 4:35 on LeClair's second goal of the playoffs.
While being pulled down in the slot, Tony Amonte unleashed a shot that Lalime stopped. Defenseman Curtis Leschyshyn got to the crease but could not control the rebound or LeClair, who buried it for a 1-0 lead.
With 7:12 to go in the first, Simon Gagne tried to give the Flyers a two-goal advantage by recreating his Game Two goal.
Gliding down the left side, Gagne came around the net to the right side before putting a shot on net. Unlike Sunday, Lalime was able to corral it and keep the deficit at 1-0.
With the teams skating four aside to start the second, Claude Lapointe was called for interference 42 seconds into the period, giving the Senators a rare 4-on-3 advantage.
After Redden's slap shot from the blue line was blocked by Flyers captain Keith Primeau, the puck came to Alfredsson, who slipped a shot from the left circle under Cechmanek's right pad at 1:06 to even the game.
"That's something we missed in Game Two that we could have capitalized on," Alfredsson said of the Senators' power play, which was second overall during the regular season. "Tonight, it was the difference."
"I talked with the team about how specialty teams and goaltending is often key in the playoffs," Ottawa coach Jacques Martin said. "I saw how in Game Two, that it was what probably lost us the game. We had some opportunities that we didn't create on and weren't effective with. The power play had been our bread and butter all year. Tonight, it was a factor."
Despite only scoring one goal this postseason, Amonte continued to set them up.
From behind the net, Amonte fed Kapanen for a one-timer from the slot. Lalime made the initial save, but the puck popped into the air before bouncing off the goaltender's left shoulder and into the net at 12:46 for Kapanen's fourth tally.
While tackling defenseman Zdeno Chara and crashing into the boards headfirst late in the period, LeClair was given a holding penalty that carried over into the third.
The Senators wasted little time converting as Hossa caught Cechmanek out of position 22 seconds in for his fifth goal of the postseason.
Grabbing a loose puck behind the net, Hossa skated around to the left post. As Yushkevich inadvertently restricted the use of his stick, Cechmanek was unable to move across the crease in time to prevent Hossa from stuffing in the puck.
"We came up on the power play," Hossa said. "There was a play to the net. I went behind the net and tried to pass their defensemen. I saw that the goalie was halfway out from the net. I knew that I could get a wraparound."
Hossa's goal marked the third time in the series Philadelphia has squandered a lead.
"It's frustrating," LeClair said. "To play against that team, you have to play with the lead. We've gone out and done that, but we have to do a better job of not sitting on it. We need to keep playing hockey and being more aggressive with the lead."
"We have to find a way to do a better job in putting them away when we have the lead," Primeau added. "We had some opportunities again tonight when it was 2-1. We are a solid team when we have a multiple-goal lead. Tonight, we didn't do that and it ended up costing us."
Chances were limited until 78 seconds into overtime, when Hossa intercepted defenseman Eric Weinrich's pass at the blue line and skated in alone before being denied by Cechmanek on an attempt to slip the puck between his pads.
While standing at the left point a minute later, Bryan Smolinski threaded a cross-ice pass to a a streaking Karel Rachunek. Cutting in alone on the right side, the defenseman could not get the puck past Cechmanek, who covered up immediately.
The Flyers had a breakaway of their own at 3:26, when Yushkevich sent Amonte in with a pass at the blue line. But Lalime did not bite on a deke by Amonte, who lost control and watched the puck roll into the corner.
"I am kicking myself in the butt right now," Amonte said. "I definitely think I should have shot. He is such a big goalie, you think you can get around him. A shot on net is always better than getting it dumped in the corner. It just rolled off my stick."