Alfredsson had two goals, including the go-ahead goal with 8:25 left, and the Senators defeated Philadelphia 6-3 to extend the Flyers' franchise-record losing streak to nine games.
The Senators were without Spezza, who suffered a knee injury against Tampa Bay on Thursday and is out indefinitely. He had scored 44 points (19 goals, 25 assists).
"We're going to have to play better defensively," Alfredsson explained. "Goals are going to be harder to come by with Spezza out.
"Paying attention to detail, especially in our own end and in the neutral zone is going to be very important. Special teams is going to have to do the job for us."
Joe Corvo, Chris Phillips, Denis Hamel, and Peter Schaefer also scored for the Senators, who had dropped two straight and six of their previous eight games.
"Defensively, we got too much spread out and teams were coming with speed on us in the neutral zone," Alfredsson said about the Senators' losses. "We had to back off and gave them a lot of time and space. Skill teams like Nashville and Detroit exploited that and made it real hard for our goalie."
Ben Eager, Jeff Carter and Kyle Calder scored for the Flyers, who set a franchise record by losing their sixth straight home game. Philadelphia had dropped five straight in 1969 and 1990.
Alfredsson broke a 3-3 tie when he knocked a rebound of a Dany Heatley shot over the stick of Philadelphia goaltender Antero Niittymaki. Heatley had stolen the puck from Philadelphia defenceman Derian Hatcher.
"As bad as we've been playing, we finally had a good third period," Heatley said. "Today the game plan was to keep the puck deep in their end. The game plan worked and we had a lot of chances."
Schaefer added a power-play goal when he put a wrist shot into a wide-open net at 12:29 and Alfredsson scored a short-handed open-net goal with 25 seconds left.
"Without Spezza we were forced to work harder," coach Bryan Murray said. "The biggest thing was the work level, getting the puck deep and then really working hard and low against their defence."
Ottawa goaltender Martin Gerber had 26 saves. Niittymaki, making his 15th straight start, stopped 36 shots.
The Flyers led 2-1 after outshooting the Senators 16-7 in the first period.
Corvo put the Senators ahead at 6:09 when he slapped a one-timer from the left circle past the pads of Niittymaki on a power play.
Eager tied it at 12:30 when he hammered in a rebound of a point-blank wrist shot by Stefan Ruzicka.
Carter made it 2-1 with 2:32 left when he connected on a one-timer from the left circle. He said that the Flyers really felt confident after the first period.
"It was pretty vocal and lively and feeling confident," Carter explained. "But when guys went out there and tried to do some things, we got set back. It's been a problem all year when we get the lead."
The Senators scored twice in a span of 1:39 to take a 3-2 lead midway through the second period. Phillips flicked a wrist shot past Niittymaki at 12:34 to tie it and Hamel converted an unassisted breakaway at 14:13 to put Ottawa back in front.
Calder tied it with 1:10 left in the period when he tapped the puck into the net from the right side of the goal after taking a brilliant pass from Sami Kapanen, who was standing at the far left baseline.
"Maybe it's a lack of confidence right now," said Kapanen about the losing streak. "Other teams are coming hard at us and we don't move the puck the way we need to and avoid the turnovers."
Philadelphia centre Peter Forsberg was scratched because of post-concussion symptoms. The Flyers are 0-9-3 when he is not in the lineup.
Notes: The Flyers three home wins are the fewest in the NHL. . . . Ottawa played 22 of their first 35 games on the road (12-9-1). . . . Alfredsson also hit the crossbar on a power play midway through the second period. . . . Heatley had two assists and extended his scoring streak to four games (three goals, four assists).