It was the second goal in two games for Parenteau, who joined the Avalanche in the offseason 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.