Alfredsson scored man-advantage goals 20 seconds apart midway through the third period and Ottawa beat Florida 4-1 on Thursday night, extending the Panthers' season-high losing streak to 10 games.
The Senators had gone 4-for-35 on the power-play in their previous five games, and just 1-for-23 in their last three.
"Those were two big goals for us," the Senators captain said. "They won us the game and that's one of the things we want to improve on, and it's nice to see it pay off."
Dany Heatley assisted on Alfredsson's 18th goal -- his second of the game -- to extend his point streak to 17 games.
"We took some heat on that - we haven't been very successful in our last few games -- and it's nice to see the big guys come through and keep that point streak alive for Heatley," said Senators forward Bryan Smolinski, who scored early in the third period to tie it at 1.
"We got a lot of momentum going off that first goal," Alfredsson said. "(Chris) Neil's pass to Smolinski got the car going and after that, we put a lot of pressure on them."
Florida captain Olli Jokinen scored his sixth of the season 15:43 in. The Panthers, who gave up the winning goal Tuesday in Montreal with four seconds remaining in overtime, are 0-7-3 during the team's longest losing streak since a club-record, 13-game slide in 1998.
"They score a goal and all hell breaks loose," said goalie Roberto Luongo, who thought Florida had played its best 40 minutes of the season -- "especially on defense."
With the game tied at 1, Florida defenseman Eric Cairns was sent off for holding 11:36 into the third. Alfredsson put the Senators up 2-1 just 28 seconds into the penalty as he finished off a passing play with Jason Spezza and Wade Redden.
Cairns stepped out of the box arguing and was promptly sent back for unsportsmanlike conduct.
Ottawa needed even less time than on its previous power play to add to the lead as Alfredsson stepped up at the right point and drove a slap shot between Luongo's pads to make it 3-1 at 12:24.
"I should have kept my mouth shut and I didn't, and it cost the team," Cairns said. "That's life under the new rules. You've really got to watch your step and your Ps & Qs."
Antoine Vermette added his fourth goal at 17:45 to increase the lead to three.
The game marked Florida coach Jacques Martin's return to Ottawa. Martin, who coached the Senators from 1995-2004, had a 341-255-96 regular-season record. He coached Ottawa to eight straight playoff appearances, though managed to win only 31 of 69 postseason games. The Senators, who fell to New Jersey in a seven-game conference final in 2003, were eliminated by provincial rivals Toronto in four of Martin's final five seasons.
The Senators, who have lost just three times in 17 games, fell 2-1 on Tuesday to Carolina, their second loss to the Hurricanes this season.
"They're a good hockey club. That's why you've got to capitalize when you get your opportunities," said Martin, whose team went 0-for-6 on the power play, including five opportunities in the second. "We had some power play chances and we didn't score. Then in the third period, we got into some penalty problems and they capitalized."
Shut out through the first two periods Tuesday for the first time since their Oct. 5 season opener in Toronto, Ottawa again failed to score through 40 minutes despite firing 26 shots at Luongo - 16 in the second.
The Senators finally broke through when Smolinski scored 2:25 into the third period, tying it at 1.
Luongo made a huge pad save on Heatley moments later to keep it tied. Ottawa enjoyed a two-man advantage for 1:33 when Panthers defenseman Shawn Hill was sent off for interference at 3:44.
"You've got to remember, this is one of the better teams in the league," Martin said. "I think we learned from that and we played with them for 40 minutes."
- Martin was given a warm ovation early when he was shown on the video scoreboard along with the message, "THANKS FOR 9 GREAT SEASONS, JACQUES." "It's nice to be welcomed to Ottawa," Martin said. "It's a great city."
- Panthers C Jozef Stumpel was a healthy scratch. Stumpel, who missed his first game of the season, has no goals and four assists in 19 games.
- Ottawa held a 45-32 margin in shots, recording 19 in the third.