But when the Coyotes pushed, the Avalanche pushed right back.
Ryan O'Reilly scored a power-play goal with 41 seconds left in overtime, and Colorado bounced back after allowing two third-period goals to beat Phoenix 4-3 on Thursday night.
"(Fighting back is) what good teams do and what we have to learn," Colorado LW Gabriel Landeskog said. "It's just about finding ways to win, and that's what we did."
O'Reilly ended it in overtime, sending a wrist shot past Smith for his ninth goal of the season and Colorado's seventh win in nine road games.
"This is a very good team, probably one of the best in the NHL, and I thought our guys did a good job of coming here and winning that game," Avalanche coach Patrick Roy said.
Phoenix dictated play most of the way, spending long stretches in Colorado's zone and sending 44 shots at Avalanche goalie Semyon Varlamov.
The Coyotes fell behind 2-0 despite dominating early and fought back late, but were hurt by two late penalties: one by Hanzal that carried over into overtime, and another by Keith Yandle that set up Colorado's winning power play.
"I thought we did a lot of good things in that game, thought we controlled a lot of the play, had upward of 75 scoring chances," Coyotes coach Dave Tippett said. "But in a tight game, mistakes matter, and when you put a team on the power play twice in overtime, it usually comes back to bite you and it did."
Two of the NHL's highest-scoring teams needed a little while to get rolling, playing a scoreless first period. Phoenix had some good chances in the opening 20 minutes but couldn't get any of its 15 shots past Varlamov.
Colorado needed 32 seconds of the second period and six seconds of a power play to break the scoreless tie.
Mitchell got it, ending up with the puck between the circles after a faceoff and whipping it past Smith for his fourth goal of the season.
That didn't bode well for the Coyotes; Colorado entered the game as the only NHL team that hadn't lost after the first period at 13-0.
Paul Stastny nearly added to it midway through the period, but Smith made a spectacular save, sliding to his right, then stacking his pads to glove the one-timer.
Benoit did get one past Smith later in the period on a shot from the point that hit the crossbar and trickled in after hitting the goalie's back. Benoit was hit in the face early in the period but returned with a bandage on his chin to score for the first time since April.
Stone finally got the Coyotes on the board with a long-distance goal, beating Varlamov with a hard shot from just inside the red line that caromed in off the left post for his seventh of the season.
The Coyotes thought they had it tied five minutes into the third period when Oliver Ekman-Larsson beat Varlamov from the left circle, but it was waved off because David Moss knocked the Avalanche goalie over after a shove by Colorado's Jan Hejda.
Phoenix kept up the pressure, and Hanzal tied it midway through the period, lifting a loose rebound over a prone Varlamov.
Vermette scored on a power play, but the lead lasted less than three minutes before McLeod tied it to send the game to overtime.
O'Reilly ended it as the clock wound down in overtime, scoring on Colorado's second power-play chance in the extra period.
"We got ourselves back in the game, but it's unfortunate we took the two penalties to give them a chance to win it," Tippett said.
The Avalanche made the most of it, winning for the 16th time in 21 games this season.
Ekman-Larsson played his 200th career game. ... The Avalanche have allowed an NHL-low nine first-period goals this season. ... The Coyotes placed D Zbynek Michalek on injured reserve Thursday with a lower-body injury. ... Colorado leading scorer Matt Duchene missed his second straight game with an oblique injury.