Colorado will look to continue its streak with Jean-Sebastien Giguere in net Saturday night against the visiting Montreal Canadiens, the team with which Roy began his storied playing career.
Varlamov made 27 saves just two days after being jailed for an alleged domestic abuse incident with his girlfriend, helping guide the Avalanche (11-1-0) to a 3-2 overtime victory over 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."
Paul Stastny scored his second goal of the game 3:36 into the extra session, and captain Gabriel Landeskog also had a goal.
"There's been a lot going on with him, with the team in the last 24-48 hours," Stastny said. "Sometimes the best thing is to just get in your comfort zone."
Roy was impressed with Varlamov's performance given the situation.
"He made some great saves, and the two goals that we gave up, they were perfect shots," Roy said.
Roy, though, will put his trust in Giguere as he coaches against his former team for the first time.
Roy spent his first 10 1/2 seasons with the Canadiens, winning the Vezina Trophy three times and leading Montreal to the Stanley Cup as a rookie in 1986 and again in 1993. He demanded a trade in 1995 and was shipped to the Avalanche, winning the Cup again that season. Roy also backstopped Colorado to a championship in 2001.
Giguere has won each of his three starts while posting a 0.67 goals-against average, including two shutouts. He most recently made 34 saves in a 1-0 win over Pittsburgh on Oct. 21.
The veteran is 6-1-0 with a 2.44 GAA in his last seven starts against the Canadiens, who had won two straight prior to Friday's 4-3 loss to Minnesota.
P.K. Subban had a goal and an assist, while Andrei Markov assisted on each Montreal goal. Defenseman George Parros played his first game since suffering a concussion as a result of a fight in the season opener.
"We didn't play a full game," forward Brian Gionta said. "We had spurts where we did it and you saw that we were successful at that time, but this league is too tough. You've got to do it for 60 minutes to get wins."
Gionta's fourth goal of the season tied the game with 9:47 left in the third, but Carey Price, who made 21 saves, allowed the winner with just over five minutes remaining.
"We tied it up and continued to push, but give them credit," said Brendan Gallagher, who scored his sixth goal in the first. "It just wasn't enough."
Peter Budaj, who spent his first six seasons with the Avs, will get the nod in net Saturday. He's won each of his two starts while posting a 0.50 goals-against average after making 27 saves in 2-0 win over the New York Rangers on Monday, but he's never faced his former team.
Montreal has won three straight meetings, though they haven't faced each other since Colorado's 6-5 shootout win Oct. 15, 2011.