Nathan MacKinnon and Paul Stastny also scored and Jean-Sebastien Giguere made 30 saves for Colorado (37-16-5), which managed a split of its four-game road trip. The Avalanche opened with a win against the New Jersey Devils before falling to the New York Rangers and Philadelphia Flyers.
"I'm proud of them," Avalanche coach Patrick Roy said. "We base our relation on trust and respect, and that's what I've got since the start of the season. Seventy-nine points … it's something that we're very happy about.
"But we're not satisfied at the same time. We've played the same number of games at home and on the road, which is great. We have 12 and 12 remaining in the season. It'll be a good challenge for us. Teams are playing well. A good example tonight, I thought the Islanders played a really good game. I don't know if it was the same from upstairs, but I thought it was a fast pace out there."
John Tavares and Lubomir Visnovsky scored power-play goals for the Islanders (22-30-8), who tried to rally in the third period after falling behind 3-0. New York fell to 8-14-8 at home.
"Same old story," Islanders coach Jack Capuano said. "We dominate the game, we don't win a hockey game."
MacKinnon opened the scoring with his 22nd goal of the season 13:04 into the game. With the teams at even strength, Landeskog stormed past Eric Boulton from the right corner before being knocked into Islanders goalie Evgeni Nabokov (22 saves) by Boulton, leaving an open net for MacKinnon. The rookie forward quickly ripped it home to give Colorado a 1-0 lead. With the assist, Landeskog extended his career-high point streak to nine games.
New York had a goal disallowed 1:17 into the second period when Thomas Vanek poked a puck in the goal crease past Giguere, but it was ruled the whistle had blown before the puck crossed the goal line.
Duchene doubled Colorado's lead with his 100th NHL goal at 7:49. The speedy forward took advantage after Islanders defenseman Thomas Hickey was caught pinching in the offensive zone. Forward Brock Nelson tried to cover for Hickey, but Duchene cruised past Nelson before tapping the puck past Nabokov to make it 2-0.
Duchene scored again 2:44 later, taking a pass from Tyson Barrie (three assists) and ripping a shot from a sharp angle in the lower right circle past Nabokov.
"They came at us pretty hard. It was pretty wide open pond hockey there for most of the game," Duchene said. "They're a good team. They can score, they showed at the end. Thankfully, Jiggy shut the door for us there."
Tavares ended New York's 0-for-33 power-play drought at 11:17 of the third period. The Islanders captain cashed in on a two-man advantage, collecting a loose puck at the right side of the net and firing a wrist shot past Giguere to make it 3-1. It was his 24th goal.
Visnovsky got the Islanders within one with a power-play goal of his own 1:07 later. Moments after Erik Johnson was whistled for slashing Frans Nielsen, Visnovsky took a pass from Kyle Okposo and ripped a slap shot past Giguere for his second goal of the season.
"It's tough to come back from three goals," Tavares said. "We've had to do it a lot this year."
Landeskog put the game away with an empty-net goal at 19:13. Stastny was credited with an empty-net goal after the game, when it was ruled that Vanek threw his stick in Stastny's direction while the latter put a shot towards the goal at 19:58.
With five goals allowed Saturday, the Islanders enter the Olympic break having allowed the most goals in the NHL (200), one more than the Edmonton Oilers.
"It doesn't feel good," Nabokov said. "Anytime you lose the game like that and the game against Calgary [4-2 on Thursday], it's two pretty similar games. As a goalie, you always feel like one extra save needs to be made, and that's exactly how I feel. Now you have to pull a little bit extra from myself, let's put it that way. I'm not going to talk about anybody else. That's why we're losing the games, because we are not getting any extra fight, any extra bitterness in ourselves. We've got to find this among ourselves."
Islanders defenseman Travis Hamonic returned to the lineup for the first time since sustaining an upper-body injury Jan. 12, a span of 12 games.