Oliver Bjorkstrand and Cam Atkinson scored, and Sergei Bobrovsky made 27 saves for the Blue Jackets (29-20-3).
"This one was real big for us," Wennberg said. "I don't know if it's must-win, but you had to find a way to get off this losing streak. Yeah, it was important."
Erik Johnson, Nikita Zadorov and Samuel Girard scored, and Philipp Grubauer made 30 saves for the Avalanche (22-22-8), who have lost four straight games and 14 of the past 17.
"The offside goal, that's on me," Bednar said. "I looked at it and looked at it, you only have so much time to make a decision. They're wanting their decision, and I look at it, I can't tell if [Anderson] tagged, I know he's in before the puck. In my opinion there, it's a go-ahead goal for them and we're taking what I consider a 60-40, 70-30 shot at offside, and if we don't get it, we have to kill a penalty, and we didn't do either."
The Blue Jackets took a 1-0 lead when Bjorkstrand scored 53 seconds into the game. He skated down the right side, faked a shot, and scored on a wraparound.