Mason Appleton scored for the Jets (35-23-1), who have lost four of five. Connor Hellebuyck allowed five goals on 26 shots through two periods. David Rittich made 10 saves in relief.
"Well, we were asleep to start the game, no question," Winnipeg coach Rick Bowness said. "So, you talk to the players and get their opinion. We were clearly asleep. … We just got embarrassed. Again, let's see how we respond."
MacKinnon scored on a breakaway 19 seconds into the first period to give the Avalanche a 1-0 lead.
Appleton tied it 1-1 at 3:12, tipping Nate Schmidt's point shot for his first power-play goal in 227 NHL games.
"They scored 19 seconds into the game. It's unacceptable," Appleton said. "We rebounded, scored a goal, tied it up, and then from there we were chasing the game once they scored their second goal. You want to give credit to them, they're a really good hockey team, but we didn't help ourselves tonight. We're a really good hockey team when we want to be. We were not that tonight.
Rantanen made it 2-1 at 4:32, scoring from the left face-off circle on a 2-on-1 rush for his NHL career-high 37th goal.
"[We had] some really good discipline, structurally sound, made them earn all their chances," Bednar said. "I thought we did a nice job on the defending side of it, moved the puck pretty efficiently tonight, so it turned out to be a pretty good performance for our group."