With time winding down, Avs defenseman Greg Zanon tried to clear the puck from behind his net, but it hit a referee's stake in the corner and bounced to Kyle Chipchura. He quickly passed it over to a wide-open Doan, who shot it over the shoulder of Semyon Varlamov.
Oliver Ekman-Larsson scored the game-tying goal for Phoenix midway through the final period, and the Coyotes won for the fourth time in five games.
Mark Olver and Matt Duchene had goals for the Avalanche, who had four days of rest but still dropped their third straight.
Just before the end of regulation, David Moss was called for holding, giving the Avs a 4-on-3 advantage to start the extra period. Smith came up big and made one sprawling save after another.
Moss' penalty came just after the Coyotes held the Avs in check when Michael Stone was called for cross-checking with 2:26 remaining in regulation.
The Coyotes came up big killing penalties all game.
Colorado had a chance to gain some breathing room midway through the final period when Jamie McGinn skated in on Smith, only to have his shot turned aside by the goaltender.
The Coyotes quickly flew up ice, getting the puck to Ekman-Larsson near the blue line and letting him go to work. He weaved into the zone and sent a liner through a defenseman and right by Varlamov to tie the game at 2 at the 11:39 mark.
The goal-starved Avalanche finally got their offense cranked up in the second period as Olver scored his first goal of the season. Three minutes later, Duchene slipped the puck past Smith on a breakaway to give the Avs a 2-1 lead.
Keith Yandle nearly tied it late in the second period, only to have his shot from the blue line clang off the post and straight to Varlamov, who quickly covered it up. The referees took a look on replay but upheld the ruling on the ice of no goal.
Phoenix had a 5-on-3 advantage for the final minute of the middle period, with Mikkel Boedker having the best scoring chance when he corralled the puck down low. He attempted to lift it over a sprawled-out Varlamov, only to have the puck carom off the post and high into the air to end the period.
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It was a fight-filled game with Cody McLeod squaring off against Chipchura and Patrick Bordeleau later dropping the gloves and going after Paul Bissonnette. All were give five-minute majors for fighting.
Doan scored his first goal in eight games midway through the opening period when he circled around the net and sent a backhand shot at Varlamov, which trickled through the goaltender's pads.
Early on, Colorado struggled to get anything past Smith, who was coming off a 1-0 shootout win at San Jose on Saturday in which he stopped 33 shots.
Smith has been difficult for the Avs to solve of late. He entered the game with a 6-1-1 mark and a 1.55 goals against average.
That's how it's been going for the injury-plagued Avs, who have already been shut out three times this season. They were missing a chunk of their offense against Phoenix because captain Gabriel Landeskog missed a seventh straight game with a head injury and forward John Mitchell was sidelined with the flu. Steve Downie is out for the season with a torn ACL.
"Got to go out there and just play the hand you're dealt," Avs coach Joe Sacco said. "We can't worry about who's here and who's not in the lineup."
The team recently went out and claimed Aaron Palushaj off waivers from Montreal, just to add a little more sizzle to their offense. Palushaj played in his first game in an Avs sweater on Monday.
NOTES: Coyotes D Rostislav Klesla played in his 600th game. ... The Coyotes are 15-1-2 in February over last two seasons, including 4-1-1 this season. ... The Avalanche closed out a four-game home stand with a 1-2-1 mark.
Press; By PAT GRAHAM]
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