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The Senators defenceman scored twice in the last 8:48 and Anderson stopped 33 shots in Ottawa's 2-1 victory over the Florida Panthers on Thursday night.
"It was a tight game," Karlsson said. "We stuck in there and finally got a crap goal, if I can say it like that. Both goalies played really well. We put as many pucks to the net as we could and finally one snuck in and that was all we needed today."
Anderson, a backup in Florida for two seasons, came within 4:13 of his second shutout since being acquired from Colorado on Feb. 18. Anderson, who has started every game since going to Ottawa, has allowed one goal or fewer in seven of his nine starts.
"A win's a win, we'll take the two points," said Anderson, 3-0-1 in five career games against his former team. "A shutout is a great accolade to have, but the more important thing is the team got the win and everyone's happy in the room."
Anderson outdueled his former goalie partner in Florida, Tomas Vokoun, who stopped 37 shots.
"It's great to get two points and get the win and coming into an old barn, I used to play on the other side, that means a little bit more," Anderson said. "There's not a whole lot of guys on that team that I've played with, but I do still know some on that team. It's good to shut those guys down and come out of here with a 'W."'
Defenceman Clay Wilson scored for Florida.
Karlsson opened the scoring at 11:12 of the third with his 10th goal of the season. He took a loose puck along the boards, skated in on Vokoun and fired a quick shot from a sharp angle. The puck trickled in after getting through between Vokoun's left arm and his body.
"It's nice to get 10 goals," Karlsson said. "It's a big accomplishment for me. I just tried to get it far post and saw it roll in from behind the net."
With Ottawa on the power play, Karlsson scored again with 5:10 left. He put home a rebound after Vokoun stopped Gonchar's slap shot from the point.
Wilson scored his second goal in the last two games to close the gap to 2-1. He swept the puck past Anderson after Niclas Bergfors' pass toward the net was deflected.
Wilson, who has spent most of the season in the AHL, also scored Tuesday night in Florida's 3-2 victory over Chicago.
Early in the third period, Ottawa killed a five-minute Florida power play after Francis Lessard was given a major and game misconduct when he appeared to leave his feet and checked Scott Timmins in the head area.
Timmons didn't return to the game after the hit and will be re-evaluated Friday for a possible concussion
The Senators killed off four power plays in all, extending their streak to 31 consecutive penalty kills.
"Special teams were huge," Ottawa coach Cory Clouston said. "Our penalty kill was very solid. It was nice to see our power play ended up getting the winning goal."
Ottawa has won all three meetings between the teams this season. The Senators won the first one 5-3 on Oct. 28 and took the second 5-1 on Feb. 23 in Anderson's second game with the team.
NOTES: Sergei Gonchar's assist on Karlsson's second goal was the 500th of his NHL career ... Florida D Alexander Sulzer missed his third consecutive game because of an upper-body injury ... Ottawa has won 15 of its last 18 games at the BankAtlantic Center ... The Panthers played their league-leading 42nd one-goal game. They are 17-16-9 in those games ... After the game, the Senators headed north to Tampa, Fla., where they'll play the Lightning on Friday night (7:30 p.m., Sportsnet Sens, Team 1200).