Rantanen and Nazem Kadri scored, and Darcy Kuemper made 22 saves for Colorado (32-8-4), which had won 10 straight but is 15-0-2 in its past 17 games.
Alex Galchenyuk scored his first of the season and the deciding goal in the second round of the shootout for Arizona (11-29-4), which had lost five straight. Wedgewood made 38 saves.
"We mentioned many times this year that we have a group with a lot of pride, a lot of character and a lot of leadership," Coyotes coach Andre Tourigny said. "The boys take pride in the way they play, the way they bounce back. They know the [Avalanche] are a really good team; they were on a roll. They arrived here with a lot of pride, they played with a lot of passion, and they battled all the way through."
Kadri gave the Avalanche a 1-0 lead at 2:42 of the second period when he intercepted a pass by Christian Fischer, skated through the slot and put a backhand over a sprawling Wedgewood.
Galchenyuk, who was playing his 24th game this season, tied 1-1 at 12:54. Ilya Lyubushkin passed to him near the right hash marks for a backhand that went through the legs of Nick Schmaltz.
"I put in the work trying to find my game, put a lot of effort on my two-way game," Galchenyuk said. "Over the last few games, my game's really been building a lot better and better and I had a great opportunity tonight."