Jonathan Quick made 23 saves for the Kings, who registered their first road playoff victory in Chicago in eight tries.
Corey Crawford stopped 18-of-19 Los Angeles shots through 40 minutes before surrendering four goals on 11 shots in the third.
The Blackhawks suffered their first home loss in this postseason.
Game 3 is Saturday in Los Angeles.
Celebrity Families of 2014 [PHOTOS]