Anderson, who signed as a free agent with the Avalanche in the offseason, stopped 35 shots, and Colorado beat the Vancouver Canucks 3-0 on Saturday.
It was Anderson's eighth career shutout and his first since beating Edmonton 2-0 on Dec. 11, 2008, when he was with Florida.
"It's only two games, let's not get ahead of ourselves," Avalanche coach Joe Sacco said. "But he's come up big in both games."
Anderson, who's stopped 73 of 75 shots in his first two games with Colorado, was strong throughout. He made a glove save on a blistering slapshot by Alexander Edler in the first period and poked the puck away from Daniel Sedin on a breakaway in the second.
"You don't really think. When you think you're going to hurt yourself," Anderson said. "I just tried to read and react. When he went to his backhand I went to my stick."
Wolski gave the Avalanche a 1-0 lead by finishing a nifty offensive display by his linemates. Hejduk got the puck at the blueline, fed it to Stastny who slid it across the crease to Wolski as he was getting checked. Wolski chipped the puck into the open net for his third goal of the season.
"They're providing a lot of offense," Sacco said of his top line. "We expect them to produce for us offensively."
After not generating a shot on their first two power plays, the Avalanche cashed in 6 seconds into their third opportunity. Hejduk sent a pass to the right of the net and Stastny redirected it over Roberto Luongo's left pad for his first goal of the year and fourth point.
"We've played together before," said Stastny, who has four points in the first two games. "I've always played well with Wooly, and Hedjie's a smart player. When you play with smart guys you know where you're going to be."
Rookie Matt Duchene nearly made it 3-0 later in the second on a shorthanded chance, but Luongo made the save.
Colorado eventually took a 3-0 lead on Tucker's power-play goal with 14:37 left in the game, his second goal of the season.
"We good opportunities, missed opportunities and they were able to get the first score on a bad change on our part," Vancouver coach Alain Vigneault said.
Luongo had 24 saves for Vancouver.
The Canucks, who are 0-2-0, pressured the Avalanche after falling behind 3-0, but Anderson stood tall. In one sequence, he lost his stick midway through the third but made a kick save on a shot by Sedin. With 2:52 left, Mason Raymond tried to stuff the puck under Anderson but the goalie made the save to preserve the shutout.
"I worked with him in Florida the last few years," Luongo said of Anderson. "He's a good goalie, very good goalie -- underrated. If you want to get goals on him you've got to get more traffic in front of him."
The Avalanche are 2-0-0 for the first time since the 2001-02 season. ... Colorado plays 11 of its next 13 games on the road. ... Vancouver was 0 for 3 on the power play. ... The teams combined for 42 penalty minutes, including two fighting majors each in the last 13 seconds of the game.