Duchene gave the Avalanche a 2-0 lead with his 100th career goal 7:49 into the second period and added what turned out to be game-winner less than 3 minutes later.
The Isles mounted a rally with third-period goals from John Tavares and Lubomir Visnovsky during a 5-on-3 power play, but Colorado hung on down the stretch and Gabriel Landeskog added an empty-netter to seal the outcome.
Semyon Varlamov stopped 30-of-32 shots as the Avs wrapped up a pre-Olympics road trip with a 2-2-0 mark.
Nathan MacKinnon also scored for Colorado.
Evgeni Nabokov made 22 saves for New York, which dropped a seventh in eight games.
Notable deaths of 2014 [PHOTOS]
Michael Sam cut from the Dallas Cowboys