Connor Hellebuyck made 37 saves for the Jets, who have won two straight and improved to 3-3 in their last six games.
Philipp Grubauer stopped 14 shots for Colorado, which had ended a six-game skid with a 6-1 win over the Rangers on Friday.
The Jets scored three times on the power play and once short-handed to lead 4-3 after the second period. They led 4-1 early in the second, but the Avalanche scored twice late in the period.
Copp scored at 3:59 of the third and Scheifele made it 6-3 after Wheeler intercepted a pass and sent the puck to him on a breakaway. Scheifele's shot hit Grubauer, the puck flew up and Scheifele swatted it into the net at 11:12 for his 23rd of the season.
Landeskog scored with just over three minutes remaining.
Barrie stretched his point streak to five games with one goal and seven assists. ... Trouba finished Winnipeg's scoring with an empty-net goal on the power play with 1:06 remaining.
Avalanche: Continue five-game trip at Calgary on Wednesday night.