Alfredsson scored two goals on seven first-period shots Saturday night in the Senators' 4-2 victory over the New York Rangers.
"We wanted to come back (after a 5-4 loss at Tampa Bay on Thursday) and play some good hockey," said Alfredsson, who scored his 11th and 12th goals.
Radek Dvorak and Petr Nedved, with his 200th NHL goal, replied for the Rangers.
"We weren't reading the play well," Rangers coach John Muckler said. "There was a lot of twisting and turning going on and we gave up too many opportunities."
New York goalie Mike Richter, nursing a sprained left knee, was forced into action. Kirk McLean, who has a 5-2 career record against Ottawa, was scheduled to start but was scratched because of the flu.
Richter was outstanding as Ottawa outshot the Rangers 23-9 in the first period, one shy of tying a club record for shots in a period. The Rangers were outshot 47-26 for the game.
"Every game right now is a playoff game," said Richter of the Rangersclinging to eighth place in the Eastern Conference. "There was a little pain (in the knee), but this is a good way to find out if it's ready to go."
Dvorak opened the scoring on a 2-on-1 rush with Nedved 4:05 in when he beat Patrick Lalime, who earned all four wins against the Rangers this season. Lalime made his first start in six games.
New York was outshot 11-2 before Alfredsson tucked the puck past Richter on the short side at 8:09. Then Alfredsson capped a beautiful passing play from Vaclav Prospal and Rob Zamuner on a power play at 12:35.
"It feels good," Lalime said. If not for Richter, we could have had seven or eight goals."
Nedved tied it 2-2, firing a shot over Lalime's shoulder at 9:46 of the second.
New York's all Czech Republic line of Nedved, Dvorak and Jan Hlavac accounted for four of the Rangers' five points and has piled up 73 points in 26 games.
Bonk capped a 2-on-1 with Marian Hossa to make it 4-2 with 4:04 remaining.
"I don't think we should put too much emphasis on this game," Alfredsson said. "It's a step in the right direction."
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