Miles Wood, Zach Parise, Josh Manson and Valeri Nichushkin scored for the Avalanche.
David Gustafsson and Mark Scheifele scored for the Jets.
Connor Hellebuyck made 27 saves for Winnipeg.
David Gustafsson gave the Jets an early lead 3:15 into the opening stanza converting a rebound off a Dillon DeMelo point shot to make it 1-0 Jets.
The goal was his first of the playoffs.
Miles Wood scored off a faceoff win just under two minutes into the second when Ross Colton got the disc to Wood who snapped it past Hellebuyck, beating the Winnipeg netminder between the pads at 1:59.
The Jets killed off a four minute Colorado power play after Kyle Connor clipped Cale Makar and drew blood.
Mark Schiefele gave Winnipeg the lead just over a half minute after the penalty expired, finishing off a three-way passing play off the rush when he redirected a Gabe Vilardi pass on his backhand one handed, beating Georgiev high blocker side to give the Jets a 2-1 lead.
The goal was his second of the playoffs.
Colorado then erupted for three goals in a 5:39 span late in the second period.
Artturi Lehkonen started the offensive onslaught at 14:16 when he redirected a Cale Makar shot from the point to tie it up.
Zach Parise gave Colorado the lead at 17:20 when he snapped the puck into a largely open net after Jets goaltender Connor Hellebuyck misplayed a puck beside the net.
Andrew Cogliano fed Parise from behind the net and the veteran forward did the rest, snapping up his own rebound to make it 3-2.
The goal was his first of the playoffs.
Josh Manson scored with seven seconds remaining in the second on a breakaway, sliding the disc between Hellebuyck's legs to make it 4-2 at 19:53.
Winnipeg got a power play with 7:35 remaining in the third but were unable to score.
Valeri Nichushkin added an empty netter with 56.7 seconds remaining to seal the win for the Avalanche.
Game 3 goes Friday night in Colorado.
SHOTS-COLORADO WINNIPEG
ATTENDANCE-15,225
