Colorado forward Mikko Rantanen's point streak ended at 14 games. He had 27 points (eight goals, 19 assists) in the streak.
Anders Lee and Jordan Eberle each had a goal and an assist, and Johnny Boychuk and Valtteri Filppula scored for the Islanders (16-12-4), who started a four-game Western Conference road trip with their second win in a row and third in their past five games.
WATCH: [All Islanders vs. Avalanche highlights]
Gabriel Landeskog scored, and Semyon Varlamov made 17 saves for the Avalanche (18-10-6), who are 1-3-1 in the past five games.
The Islanders limited the Avalanche's high-scoring line of Landeskog, Nathan MacKinnon and Rantanen to a power-play goal and an assist.
"Everybody knows they're the engine of the whole team," said Greiss, who is 7-2-1 against Colorado. "If you can shut them down, it's a big part of their game. It was huge to play really well against them. We didn't give them much."
Rantanen was more concerned with the loss than the end of his streak.
"Yeah, it's a long time," he said. "My linemates have been helping, like I say in every interview. The team has helped me too. I don't really think about it too much. There's so many games left, and our goal is to stay in the top three in the (Central) division and make the playoffs."