Erik Johnson and Tyson Jost scored for the Avalanche (7-6-3), who lost their fifth straight game. It's Colorado's longest losing streak since a seven-game streak from March 18-29, 2017.
"I think leaders on this team got to get on this now," Johnson said. "We've got to stop the bleeding and string some wins together here."
Semyon Varlamov made 19 saves.
"Too many mistakes and turnovers with the puck led to chances against," Avalanche coach Jared Bednar said. "But you know, all those odd-man rushes and scoring chances against, it's mostly on us, not on them."
Connor made it 1-0 eight seconds into a Jets power play at 10:16 of the first period. Scheifele's shot from the slot was blocked, but Connor was able to chip the loose puck past Varlamov.