The performance was quite a reversal for Varlamov, who allowed seven goals on 21 shots Friday in a 7-0 loss to the Vegas Golden Knights.
WATCH: [All Hurricanes vs. Avalanche highlights]
"That was a really tough game mentally," Varlamov said. "I thought I had a good start to that game and then everything collapsed. It is what it is. There are no easy games. If you have a bad game, the next night you have to bounce back, so I had to forget about it and then just keep going.
"I feel not bad, actually. Sometimes you face 30 shots and you're exhausted after the game. You never know how your body is reacting."
Defenseman Patrik Nemeth scored his first career NHL goal in 118 games and had an assist for the Avalanche (7-5-0), who are 5-1-0 at home.
"To get the win is the most important thing," Nemeth said. "It's been way too long since I scored. My role is to play solid defense, get the puck out of our zone. If I score, it's great. If not, I hope I'm doing my other job well. "
The Hurricanes (4-5-2) took 60 shots but lost their third consecutive game (0-2-1).
"Well, I'd have to look at some of them," Carolina coach Bill Peters said. "I know on the power play, the shots ... nobody at the net. A couple times we could've been at the net, in his eyes, and we weren't. If he sees it, he's a good goaltender. Looks like he's going to make the save."
The game didn't start well for Varlamov. Victor Rask gave the Hurricanes a 1-0 lead 55 seconds into the first period with a shot from the goal line that beat him to the short side.