Nick Leddy added a goal and an assist while Bryan Bickell and Marcus Kruger also scored for the Blackhawks, who improved to 2-1-1 on a six-game road trip.
Corey Crawford stopped 31-of-34 shots to earn the victory.
Anze Kopitar notched a goal and two assists for the Kings, who lost a fourth straight and fell to 1-8-1 in their last 10 games.
Tyler Toffoli added a goal and an assist and Drew Doughty scored for Los Angeles.
Jonathan Quick turned aside 25-of-30 shots.