Milan Hejduk scored the only shootout goal for Colorado, which had its three-game winning streak end.
Kane scored for the Blackhawks in regulation, and Patrick Lalime had 22 saves.
Andrew Brunette scored his ninth goal of the year and goalie Jose Theodore had 22 saves in his seventh straight start.
The Avalanche played without center Paul Stastny, who will miss at least two weeks after having an appendectomy Thursday. Stastny was selected to represent the Avalanche in the All-Star Game in Atlanta on Jan. 27 but will not play.
Kane gave the Blackhawks the lead just 2:32 into the game with his 11th goal of the season. Kane got behind the Avalanche defenders and Martin Havlat hit him with a pass at Colorado's blueline.
Brunette tied it midway through the first period when he knocked in his own rebound over Chicago goalie Patrick Lalime, who was reaching for the loose puck.
Each team had chances to take the lead in the second period. Rene Bourque got a step on the Colorado defense as he entered the Avalanche zone, but before he could get off a shot, defenseman John-Michael Liles made a diving poke check.
