Fisher sent a cross-ice pass to Redden, who beat goalie Antero Niittymaki to give the rejuvenated Senators their third straight victory. The Senators, who entered with the third-worst record in the Eastern Conference after piling up 119 points last season, won for the fourth time in five games.
Petr Nedved got his first goal of the season and Mike Knuble also scored for the Flyers, who lost their sixth straight home game and third in a row overall just hours after former coach Ken Hitchcock was hired by the Columbus Blue Jackets.
Last month, Hitchcock was fired and general manager Bob Clarke stepped down after the Flyers got off to a 1-6-1 start.
Next up for the Flyers is a game against Hitchcock and the Blue Jackets on Friday afternoon in Philadelphia.
The Flyers built a 2-0 lead by early in the second period, but the Senators fought back.
Fisher cut the deficit to one, scoring a power-play goal just more than four minutes later. Fisher beat Niittymaki with a well-placed wrist shot into the top right corner for his third of the season.
Alfredsson tied it at 2 in the last minute of the second, sending a low wrist shot past Niittymaki with 33.6 seconds left in the period.
In a wide-open third period, the Flyers had several scoring chances. Randy Robitaille just missed twice from close range, and Simon Gagne also had two chances, but both were directed just wide.
Ottawa, which failed to convert on two power-play chances, had its best scoring chance with just seconds remaining, but a hard shot by Joseph Corvo was tipped over the net.
In a matchup of struggling Eastern Conference teams, the play at the outset was wide open, albeit less than stellar. It seemed only right that a fluke goal punctuated the opening period.
The Senators got off 13 shots against Niittymaki, while the Flyers put 10 shots on Ottawa's Ray Emery, the last of which counted most.
The Flyers took the early lead on Nedved's first, when Geoff Sanderson pushed a rebound Emery couldn't handle to the right side. Nedved scooped up the puck and sent a shot back through the crease that ricocheted off the skate of a Senators player and into the net.
Just more than four minutes into the second, Knuble made it 2-0 with his sixth goal. Emery stopped a shot from a tough angle and pressed his flattened leg pad against the post, but the puck bounced up and Knuble slapped it in.
Notes: Flyers captain Peter Forsberg was scratched from the lineup. He missed practice on Tuesday because of a stiff lower back and is day to day. Forsberg was injured when he hit the boards during Monday's loss to Pittsburgh. He slipped into the boards when his ailing right foot, which has caused him so much trouble this season, gave way. The team continues to search for a solution for Forsberg's surgically repaired right foot. He has six goals and seven assists in 21 games. Defencemen Mike Rathje and Alexandre Picard were also scratched. ... Ottawa scratched Denis Hamel. ... The Flyers recalled forward Eric Meloche from the Philadelphia Phantoms of the AHL before the game. In four earlier games with the Flyers, the five-foot-10, 200-pound Meloche had two assists. ... Left wing Triston Grant was sent down to the Phantoms. He had an assist and 10 penalty minutes in eight games with the Flyers.