Nathan MacKinnon and Cale Makar each had two assists, and Pavel Francouz made 27 saves for the Avalanche (34-18-7), who were 0-2-1 in their previous three games and moved within one point of the Dallas Stars and St. Louis Blues for first place in the Central Division.
"We needed to get back on the winning side of things," Colorado captain Gabriel Landeskog said. "The homestand has been a little bit up and down and we found ways to lose games. This was well needed and big to finish up the homestand this way."
WATCH: [All Islanders vs. Avalanche highlights]
Semyon Varlamov made 26 saves in his return to Colorado for the Islanders (33-20-6), who were outscored 11-2 during their four-game road trip and remained tied with the Carolina Hurricanes and Columbus Blue Jackets for the first wild card into the Stanley Cup Playoffs from the Eastern Conference.
"We're not obviously scoring," New York coach Barry Trotz said. "They jumped on us early. They came out with a better purpose at home and their big guys were dangerous early. We gave up a goal, I thought [Varlamov] kept us in it in the first. Our game settled down in the second and third, but it's not coming easy for us.
"Right now, we're going through some adversity, some guys are drying up and we need people to step up. All that being said, the only people that are going to help us are the people in the room, our group, and we're just going to have to find a way. We can't do anything to repair this trip, but we can repair our next game and the following game."
Joonas Donskoi scored his NHL-career high 15th goal to give Colorado a 1-0 lead at 9:07 of the first period when he redirected Makar's shot from the blue line in off the right post.
"We got after them and created a lot of scoring chances," Landeskog said. "This is a team that you need to get a lead on and score first because they're so well structured defensively. If they get a lead, they're not going to give up much."