The Avalanche are expected to continue that trend with Varlamov drawing the start in their attempt at the best start in franchise history Wednesday night against the Nashville Predators.
Colorado coach Patrick Roy made a controversial move Friday by starting Varlamov two days after he was arrested for alleged domestic abuse. Allowed to travel with the team following one night in jail, the team's No. 1 goaltender stopped 27 shots in a 3-2 win in Dallas.
"I think I am the luckiest guy in the world because I play in the NHL and I play for this team," Varlamov said. "I've got such good teammates, so I don't think about what's happening."
After Giguere helped lead them to a 4-1 win over Montreal on Saturday, the Avalanche will turn to Varlamov again as they try to improve to 13-1-0 for the first time. In their final season before moving to Colorado, the Quebec Nordiques went 12-1-0 to begin 1994-95.
The Avalanche are also seeking their first seven-game win streak since an eight-game run Dec. 31, 2005-Jan. 17, 2006.
Roy said Varlamov will start Sunday against Washington, the finale of a four-game homestand, after Giguere plays Friday versus Calgary.
"There's been a lot going on with (Varlamov)," center Paul Stastny said. "Sometimes, the best thing is to just get in your comfort zone. ... When he's on the ice, when he's in net, he's focused on what he does."
Colorado is expected to get forward Jamie McGinn back in the lineup for its pursuit of a season-high fourth straight home win, but veteran Alex Tanguay is expected to miss at least two weeks with a knee injury. An ailing knee kept McGinn out of the past three games.
Colorado also seeks a fourth consecutive home win against Nashville (7-5-2) after posting a 3-1 victory Oct. 4. P.A. Parenteau scored two goals and Varlamov stopped 26 shots as the Avalanche won for the third time in four overall matchups.
Parenteau snapped a nine-game goal drought Saturday, and Nathan MacKinnon scored the tiebreaker with 11:59 remaining.
"We're 12-1, and everyone in this locker room feels like we're not satisfied," MacKinnon said. "That's the exciting part, that we can get better; 12-1 is great, but 13-1 is even better."
The Predators avoided a season-high third consecutive loss Saturday by bouncing back quickly from a blown two-goal lead for a 4-3 win in Los Angeles. David Legwand's second goal of the game with 3:56 left broke the tie.
"I think it says a lot about us, especially the way it worked out after blowing a two-goal lead," goaltender Carter Hutton said. "They had all the momentum, and the crowd was behind them, but we kept to our game. Getting one late was huge for us, making it 4-3 and holding on for the win."
With Pekka Rinne out due to a hip injury, Nashville's goaltenders have a combined seven games of experience - none against Colorado. Marek Mazanec, called up from the minors Tuesday, has never appeared in an NHL game.
Varlamov has allowed one goal in his last two games against Nashville. He outdueled Rinne in a 1-0 overtime victory in Denver on March 30.