Brandon Saad and Brent Seabrook also scored for the Blackhawks, while Patrick Sharp celebrated his 33rd birthday with a game-sealing goal in the third period. Kane added an empty-net goal with 5.4 seconds remaining.
This is the second time Chicago has beaten Colorado at Pepsi Center this year after going 0-2 in the building last season.
Crawford wasn't challenged all that often in the third period, but came up big with the Avalanche on a 5-on-3 power play. He stopped a point-blank shot with his shoulder to help the Blackhawks successfully dodge both penalties.
Stay Connected
NHL.TV™
NHL GameCenter LIVE™ is now NHL.TV™.
Watch out-of-market games and replays with an all new redesigned media player, mobile and connected device apps.
Introducing the new official NHL App, available for iPhone, iPad and Android smartphones and tablets. A host of new features and improved functionality are available across all platforms, including a redesigned league-wide scoreboard, expanded news coverage, searchable video highlights, individual team experiences* and more. The new NHL App on your tablet also introduces new offerings such as 60fps video, Multitasking** and Picture-in-Picture.
*Available only for smartphones
** Available only for suported iPads