In a meeting of teams that will miss the playoffs, Colorado overcame an early two-goal deficit and twice let a one-goal lead slip away.
Colorado will finish with the worst record in the Western Conference and the second-worst in the NHL behind Florida. The Avalanche, however, still have a say in which team grabs the final playoff spot in the West because they will host Minnesota Saturday -- and the Wild will need a win to ensure a trip to the post-season.
David Schlemko and Antoine Vermette gave Phoenix a 2-0 lead in the first period, but it took a power-play goal from Vermette 5:56 deep in the third period to forge a 4-4 tie.
Parenteau scored one of three consecutive Colorado goals in a span of 4 minutes late in the first period to get the Avalanche back in the game.
Mike Smith gave up the two shootout goals for the Coyotes.