Colorado came up big against Chicago last spring, and repeated that performance Tuesday night.
Varlamov stopped 36 shots and Paul Stastny had a goal and an assist for the Avalanche in a 5-1 victory over the Blackhawks.
Gabriel Landeskog and John Mitchell also scored during Colorado's three-goal first period. P.A. Parenteau and Cody McLeod added goals in the second and third for Colorado, which snapped a three-game skid.
"You always say a win is a win, and it is. But at the same time our strength is our team morale and confidence," Landeskog said. "It feels good. It doesn't mean anything unless we go into Phoenix and play well."
Brandon Saad scored for the Blackhawks, who failed to get at least two goals for the first time this season. Colorado ended Chicago's NHL-record streak of 24 consecutive games with at least a point to start a season in a 6-2 win last March.
"Maybe we tend to respect them a little more than other teams, which we shouldn't," Stastny said. "We should respect everyone the same way. When you're young, that happens. They're the defending champs and you always want to play your best against the best."
"The target all the time was that someday I could play in the NHL, and in Rockford I had good games there, and I know I can do it," he said. "Only now it's the small things, so we have to keep doing work and prepare to be even better all the time."
The Blackhawks had their opportunities in outshooting Colorado 37-23. They had several quality chances to get back in the game in the second period but couldn't put one past Varlamov.
Colorado stumbled after winning 14 of its first 16 games but capitalized on its chances in the first period this time. Stastny scored when Brent Seabrook's pass off the boards ricocheted to him in the slot, and he beat Crawford with a slap shot.
Landeskog gave Colorado a two-goal lead when he redirected Andre Benoit's shot from the point past Crawford with 7:39 left in the period. Just 56 seconds later, Mitchell made it 3-0.
"We had a really good start. We were really sharp around the net and scored nice goals," Avalanche coach Patrick Roy said.
Raanta, recalled Sunday, replaced Crawford after Mitchell's goal. He faced only seven shots over the next 25 minutes but allowed his first goal late in the second period.
After the Blackhawks had several strong chances in front of Varlamov, Parenteau skated down the left boards and beat Raanta with a shot from the circle to make it 4-0 with 1:22 left in the second.
"The fourth goal was big for us. They were buzzing in our zone and Varly made some key saves for us," Roy said. "You're always afraid being up 3-0 of having a letdown. But we were moving our feet."
McLeod scored his first goal of the season on a rebound 1:44 into the third.
Chicago lost forward Bryan Bickell in the first period after he crashed into the Avalanche net. He didn't return, and coach Joel Quenneville said after the game that Bickell might be more than day-to-day.
"But I'm not sure of that," Quenneville said.
It's a tough blow for the Blackhawks, who are playing without forwards Michael Handzus and Marian Hossa.
"Bicksie is obviously a big part of this and you hope it's not too long," Kris Versteeg said. "Obviously, we need him in the lineup."
Colorado forward Maxime Talbot and defenseman Tyson Barrie had two assists each. ... There were only two penalties called in the game, one on each team. ... Avalanche C Matt Duchene is expected to miss at least a week with an oblique injury sustained in Saturday's loss to Florida. ... Hossa missed his third straight game with a lower-body injury. ... Colorado placed forward Alex Tanguay (knee) and defenseman Ryan Wilson (back) on injured reserve and recalled C Brad Malone and Barrie from Lake Erie of the AHL.