Jeff Tambellini had a goal and an assist while Bruno Gervais, Dean McAmmond and Jesse Joensuu each had a goal for the Islanders, who have won their last two games.
The Islanders scored the only goal of the first period with 6:45 left in the frame as McAmmond's wrister from the top of the right circle squeezed between the pads of Raycroft.
Colorado tied the game with a power-play goal just 33 seconds into the second. Milan Hejduk had the puck at the top of the left circle and dished it to the low left side for Paul Stastny, who sent it over to the right for an easy slam by Smyth.
The Islanders answered less than two minutes later as during a scrum in front Joensuu slammed the puck into the net for his first career goal in his first career game.
New York took a 3-1 lead with 6:56 left in the second. On the fly, Jon Sim let loose with a wrister from the right circle that Raycroft stopped, but the rebound went out front where Gervais slammed it home.
Colorado made it a one-goal game just 1:02 into the third period on Smyth's wraparound from the right side.
However, New York was able to reestablish its two-goal lead a bit less than four minutes later. Mark Streit had the puck in his own end and raced down the ice. From the high slot he dished it over to the left side where Tambellini wristed it under the glove of Raycroft.
Colorado pulled Raycroft with less than two minutes to play and had several good opportunities in the New York end, but Danis came up with a couple of big saves to help New York hang on for the win.