The Wild were unable to contain the quickness of teenager Nathan MacKinnon, who had a goal and three assists. Stastny, the star of Game 1, also had a goal and three assists. His empty-netter sealed the win after Marco Scandella made it a one-goal game with 1:19 remaining.
Charlie Coyle also scored early for the Wild.
Game 3 is Monday in Minnesota.
Landeskog's second goal of the game gave Colorado a 3-1 lead with 8:01 remaining in the second and led the Wild to pull erratic starter Ilya Bryzgalov. Backup Darcy Kuemper stopped all 14 shots he faced, possibly opening up a goaltender controversy.
Varlamov bottled up the Wild most of the night to help Colorado hold serve at home. The Avs are 12-0 in playoff series when capturing the first two contests since relocating to the Mile High City in 1995-96.
The 18-year-old MacKinnon is having quite an NHL postseason debut. The Wild simply couldn't slow down the speedy MacKinnon, the first pick in the draft last summer. He blew past Wild defenders all evening and now has seven points in the series.
In the opening game, Colorado rallied for a 5-4 win when Stastny scored the tying goal with 13.4 seconds remaining and then the OT winner.
This time, no late-game theatrics were necessary. No bold decisions by coach Patrick Roy, either.
Roy's goalie simply played that well and only got stronger as the game went along. So, too, did the chants of ''Varly, Varly, Varly,'' from the capacity crowd.
Varlamov showed the form that led to 41 wins in the regular season, which broke Roy's team record. He allowed a late goal by Scandella, but Stastny ended any drama with his goal in the waning seconds.
Roy kept the line of Landeskog, Stastny and MacKinnon together. No surprise, really, since the trio shined since being paired late in Game 1.
They combined for 10 points on Saturday.
Landeskog scored his first goal of the game on a nifty no-look pass from MacKinnon. He added another when MacKinnon beat a Wild defender, dished it over to Stastny, who made a spin pass to Landeskog. The captain lined it over Bryzgalov's shoulder.
That was the end of Bryzgalov's night as Minnesota coach Mike Yeo sent in Kuemper.
Bryzgalov struggled in both games in Colorado, giving up eight goals on 45 shots.
Coyle put the Wild up on a crazy play early in the first period. Mikko Koivu sent a pass toward the goal that bounced off Varlamov's stick and hit a hard-charging Coyle just before he and defenseman Jan Hejda crashed into the goal, knocking the net off its pegs.
The officials reviewed the play and confirmed Coyle's second goal of the series.
Two minutes later, MacKinnon took a pass at his own blue line, flew past two Wild players at center ice, weaved between two defenders and lined a shot over Bryzgalov's arm.
The Avalanche have adopted the motto ''Why not us?'' this season, putting the mantra on shirts, ball caps and even flashing it on the scoreboard. The slogan took root when Roy posed that question when he first came on board. It was taken to heart in October after former Avs defenseman Ray Bourque addressed the team at his restaurant in Boston.
''This motto became pretty big and something we started to believe in,'' Maxime Talbot said. ''So, why not us?''
NOTES: Wild F Dany Heatley was a scratch. ... Colorado will likely be without its leading scorer Matt Duchene (knee) for this series, Roy said after the morning skate. ... Roy said F John Mitchell (head) is ''not close'' to a return. ... The Avs are now 6-0-1 against the Wild this season. ... Avalanche F P.A. Parenteau had a cut under his left eye after being hit by a stick late in the third period, but returned to the ice.