"Our offense is rolling now a little bit better," said Duchene who scored his 300th NHL point. "I think everybody enjoyed that one, everybody played outstanding. The important thing is to win and we just have to keep going."
The Avalanche set a franchise record by holding the Coyotes without a shot on goal in the second period.
"I've never seen that," Avalanche coach Patrick Roy said. "It's pretty rare. I like to give credit to our (defense). They blocked a lot of shots and did a good job protecting (goalie Semyon Varlamov)."
After the Avalanche outshot the Coyotes 27-5 and took a 5-1 lead into the second intermission, Roy replaced Varlamov with Reto Berra, who made his first appearance since Dec. 5 against the Winnipeg Jets.
"It was good to give him a bit of a rest," Roy said of Varlamov, who has started 13 consecutive games and 21 of the past 22. "He's playing a lot of games."
Varlamov said he would prefer to play every game in its entirety, but he understood Roy's reasoning.
"The schedule’s not easy and I think the coaching staff sees that," he said.
Mark Arcobello scored at 2:37 on Arizona's second shot of the third period against Berra, who finished with 11 saves.
Coyotes goalie Mike McKenna, playing his first NHL game of the season, was under siege from the start and made 29 saves. The Coyotes (20-31-7) lost their fourth consecutive game.
"Our execution wasn't at an NHL level tonight, and our work ethic was right behind that," Coyotes coach Dave Tippett said. "Hence, you get a game like that. That didn't look like an NHL game. It's tough. You're hoping (McKenna) can come in there and get us some saves. But we didn't give him much help in front."
The Avalanche outshot the Coyotes 15-5 in the first period and built a 3-1 lead on goals by Duchene, Cody McLeod and Nick Holden, whose power-play goal at 14:58 ended Colorado's 0-for-32 drought with the man advantage.
Duchene won a faceoff in the left circle and drew the puck back to Zach Redmond, who passed across to Holden for a shot that beat McKenna to the short side.
"Going forward, we need to have our power play going to make a good run and get back to the playoffs," said Holden, who scored the Avalanche's previous power-play goal Jan. 15 against the Florida Panthers. "It was a good play by Zach to drag it and come back and open me up. He put a perfect pass over and the goalie didn't even see the puck because (Alex Tanguay) had such a good screen. I just got good wood on it. I was just trying to hit it hard and get it past their blocks.
"It's something that we've been working at. It's something we're going to need. To get our playoff push going we need to get the power play going. It's nice to get that first one out of the way."
The Avalanche tied a franchise record for the fastest two goals when McLeod and Duchene opened the scoring nine seconds apart.
McLeod backhanded his own rebound past McKenna at 2:54 after Paul Carey took the original shot from the left point. The goal gave McLeod 100 NHL points. Carey's assist was his first point in 17 NHL games.
Duchene skated to the net to convert a pass from Iginla at 3:03 to stretch his point streak to four games (two goals, four assists). Iginla has two goals and five assists in his past four games.
"It shows that when we're driving the net, good things happen," Roy said. "We're working well around the net. I just like the intensity of our forecheck. I really feel we're attacking as a unit of five and I like to see that."
The Coyotes drew within 2-1 on a goal by defenseman Oliver Ekman-Larsson, who scored from the left point at 9:51. He leads NHL defensemen with 17 goals.
"That's about as poor of execution I've seen a team have in a long time," Tippett said. "We've got lots to work on. Gosh, look at the way we played. We need time to practice."
Barrie moved into the lower portion of the right circle after Iginla skated down the opposite side and stopped near the goal line. He passed through the goalmouth to Barrie, who scored at 7:28.
Landeskog was outside the crease on the left side when he took Ryan O'Reilly's pass and beat McKenna high to the stick side at 17:18.
"It's frustrating, embarrassing," Coyotes defenseman Keith Yandle said. "It's all those things, especially to come in here and not be able to get a shot in a period. It's tough. There's nothing more you can say. We've got to be better. We've just got to wipe this away clean and keep going."