Duchene scored two goals and set up another, Varlamov made 33 saves and the Colorado Avalanche beat Columbus 4-0 on Thursday night.
"He was at his best tonight," Duchene said of Varlamov. "He was our best player. He's just solid. He gives us confidence. That was an outstanding effort by him."
Varlamov preserved his ninth career shutout and first of the season when he made a sprawling save on Nick Foligno's shot late in the second period. He followed that early in the third with a stop of Ryan Johansen's shot from in close by using his chest.
"You've got to give him credit," Johansen said. "He was sturdy and strong back there. It's frustrating for our guys to not be able get one past him."
Varlamov also got an assist from the Avalanche's penalty-killing unit, which shut down all six power plays by the Blue Jackets.
Since allowing two power-play goals in a season-opening loss at Minnesota last Saturday, the Avalanche have killed 16 consecutive power-play opportunities by the opposition.
"The guys did a great job for me," Varlamov said. "They blocked a lot of shots, so I can say thanks."
The shutout was his first at home for the Avalanche after compiling four in his first season with Colorado last year.
"It's huge for me and it's huge for the team," Varlamov said.
Playing their first game since learning they had lost Steve Downie to a season-ending knee injury in Tuesday's win over the Los Angeles Kings, the Avalanche got another scare when John Mitchell took a puck off his face in the first period and left the ice holding a towel to his bleeding nose.
Mitchell was tended to by medical staff, returned to the game in the second period with a gauze wrap stuffed up a nostril and scored his second goal of the season off a feed from Milan Hejduk at 4:38 of the third.
Duchene scored on a breakaway at 18:42 of the third. He also set up the Avalanche's opening score 51 seconds into the game with a cross-ice to P.A. Parenteau, who wristed a shot from the left circle past goalie Sergei Bobrovsky.
It was the second goal in two games for Parenteau, who joined the Avalanche in the off-season as a free agent after playing for the New York Islanders last season.
Later in the first, Duchene scored his first goal of the season to put the Avalanche up 2-0. He put in a rebound after Bobrovsky blocked a shot by Hejduk but could not control the loose puck.
"Getting a couple of goals, you put them in a hole right away," Duchene said.
That wasn't how the Blue Jackets wanted to open the game.
"We have to have better starts," Johansen said. "It's tough to come back from deficits in this league. We've got to be more sharp to start games. We have to have our focus a little stronger and everybody has to be on the same page. If we do that we'll be successful. I'm not concerned, but we've got to keep working."
NOTES: After losing 5-1 in Phoenix on Wednesday, the Blue Jackets went 0-2 in the first of their 11 back-to-back sets this season. Columbus fell to 59-100-26 all-time in the second game of back-to-backs. ... It was the second time in two games that an Avalanche player was struck in the face by a puck. On Tuesday against the Kings, Duchene needed stitches to close a cut on his chin after being hit by a puck. ... It was Varlamov's second career shutout against the Blue Jackets. He also held them scoreless last season.