Mark Scheifele fed a cross-ice pass through traffic, and Connor scored with a catch-and-release wrist shot from the hashmarks for the 3-2 final at 19:00 of the third period.
Connor also scored in the second period, Cole Perfetti had a goal and Stuart Skinner made 32 saves for the Jets (3-0-1), who have points in four straight games to begin the season. Dylan Samberg had two assists.
Jaden Schwartz and Fedor Svechkov each had a goal and an assist for the Avalanche (2-1-0), who lost their first game of the season. Mackenzie Blackwood made 16 saves.
After a scoreless first period, Schwartz got a lucky break off a mishandled puck in the offensive zone to make it 1-0 Avalanche at 2:51 of the second.
Just 1:10 later, Connor tied it 1-1 at 4:01. While screening Blackwood, he scored with a waist-high tip of Neal Pionk’s point shot.
Perfetti made it 2-1 at 18:16, getting the deflection of Samberg's point shot off his left skate.
Svechkov tied it 2-2 at 12:35 of the third period. Brett Kulak’s shot went off the end boards, and Schwartz quickly fed Svechkov in front for the poke through Skinner's five-hole.
Winnipeg defenseman Josh Morrissey sustained an upper-body injury while landing a hit on Avalanche forward T.J. Hughes late in the first period. Morrissey returned for one shift of 1:32 at the beginning of the second period, but then left the game and did not return.