Back on the ice just three days after their heart-stopping Game Seven overtime win over the Detroit Red Wings, the Blackhawks had to come from behind to beat the Kings, last year's Stanley Cup champions.
The Kings, who were also taken to seven games in their semi-final with San Jose, snatched the lead in the first period despite being heavily outplayed.
Justin Williams scored against the run of play, grabbing a loose puck and sending it past Chicago goalie Corey Crawford.
The Blackhawks, who won the Presidents' Trophy for having the best record in the regular season, tied the game early in the second period.
Patrick Sharp, who has scored a league best eight goals during the playoffs, reacted quickly to score from a shot by Chicago's Johnny Oduya that rebounded off the pads of Jonathan Quick.
The LA netminder made 34 saves but gave up two goals in four minutes in the second period, the first by Sharp then the second by defenseman Marian Hossa.
Crawford turned away 21 shots for the Blackhawks, who host Game Two of the best-of-seven series on Sunday.
The Western Conference winner will play either Boston or Pittsburgh for the Stanley Cup.
(Reporting by Julian Linden; Editing by Patrick Johnston)