Alfredsson, the Senators' captain, started the comeback with a key goal late in the first period and Anderson made 37 saves in a 3-2 victory over the Toronto Maple Leafs on Tuesday night.
The win kept the Senators on a run that has seen them go more than two months since dropping consecutive games in regulation. The last time that happened was Nov. 9 and 11.
"I think it's just the character of what we have in the room," Anderson said. "Our leadership, our guys that find ways to bring it every day. You know, I think it's a credit to our captain Alfie and how he comes to the rink every day, battles hard.
"That guy never takes a day off and he's just a great role model for everybody else."
The Senators looked a little flat-footed playing for the second time in as many nights. They were coming off a 2-0 loss to Winnipeg on Monday and were trailing the Leafs by that same margin in the first period.
But Alfredsson got the comeback started, sending a backhand past James Reimer 7.5 seconds before the intermission.
"We didn't have a great first period, they took it to us a little bit," Senators forward Jason Spezza said.
"To get that goal ... it gave us a little bit of life and gave us a chance to kind of collect ourselves in the room and figure out what we have to do differently. That's what we did."
Spezza and Kyle Turris also scored for Ottawa, which heads to California for three games and Phoenix for one before hosting the All-Star game later this month.
Matthew Lombardi and Joffrey Lupul scored for the Maple Leafs.
"We let them hang around," Lombardi said. "We were getting some chances, but we didn't put them away."
The game featured two fights, including one between Leafs captain Dion Phaneuf and Nick Foligno in the second period that came six minutes after the Senators' forward had a low hit on Phaneuf.
The Senators are fifth in the Eastern Conference and have a nine-point lead over ninth-place Toronto.
"Both teams are a lot better teams than we've been the last couple years and the games mean a lot more," Spezza said. "When there's a lot at stake, the games become more intense. I think it's great for the game and great for our rivalry. They're fun games to play when you're competing like that."
Much of Ottawa's recent success can be attributed to Anderson, who wasn't forced to make any spectacular saves against Toronto and benefited from a couple of shots that hit off the post.
The NHL's player of the week is 7-1-1 in January with a .945 save percentage.
Turris also enjoyed a big night in his first career game at the Air Canada Centre.
He scored the game-winning goal early in the third period with a high shot that eluded Reimer, giving him 11 points in 15 games since coming over in a trade from Phoenix.
"We've been winning," Turris said. "It's a real fun atmosphere, we're all having a good time and working our butts off. As long as we keep winning, we're going to keep having fun."
Once the Senators clawed their way out of the early 2-0 deficit, Anderson didn't allow the Leafs another goal. The veteran goaltender earned plenty of praise from his teammates after helping secure another victory.
"He's been unbelievable," Turris said. "He's stood on his head every night for us whether we're up 2-0 or down 2-0. He's making the saves, especially when we're down — he's making the big saves to keep us in it and give us the chance to come back like tonight.
"He's playing unreal, he's definitely the backbone behind us winning here."
NOTES: Andre Petersson and Mark Borowiecki sat out for the Senators. Both were called up from Binghamton (AHL) earlier in the day and are expected to make their NHL debuts on Ottawa's current road trip, which continues Thursday in San Jose against the Sharks (10:30 p.m., Sportsnet East, Team 1200) ... Nazem Kadri was a healthy scratch for Toronto. He had one assist in his past seven games ... It was Reimer's first start since a Dec. 31 loss in Winnipeg ... Alfredsson's goal was his 32nd in 73 career games against Toronto ... The teams meet again Feb. 4 at Scotiabank Place.