The Islanders took a 3-0 lead midway through the second on a goal by Michael Graber, but Colorado rallied to end a four-game losing streak. The Islanders have dropped two in a row and their 11-point total is the lowest in the Eastern Conference.
Quincey scored the game-winner with 2:39 having gone by in overtime when he took advantage of a screen provided by David Jones. The goal came on the power play after New York goaltender Al Montoya was called for a high stick.
Paul Stastny began Colorado's comeback on a power-play goal with 21 seconds left in the middle period. Milan Hejduk brought the Avalanche within one 6:07 into the third and Jan Hejda tied it with a slap shot 4:28 later.
Jean-Sebastien Giguere made 30 saves to get the win, shutting down the Islanders for the final 32 minutes. Montoya allowed four goals on 51 shots.