Ondrej was perfect until 14:48 of the third period when Kevin Porter tipped in Colorado's lone goal.
Colorado's Jean-Sebastian Giguere allowed four goals on 26 shots. The Avalanche's eight-game home winning streak came to an end.
Kane opened the scoring at 16:37 of the first period and added his second goal at 14:52 with assists from Stapleton and Chris Thorburn.
2014 amfAR Inspiration Gala [PHOTOS]
Julius Randle breaks leg during NBA debut