Alec Martinez silenced a raucous United Center crowd when he scored the series-deciding goal 5:47 into the first extra session, his shot from the left point hitting Chicago defenseman Nick Leddy and looping past goaltender Corey Crawford.
Bidding to lift a second title in three years, the Kings move on to face the New York Rangers, who beat the Montreal Canadiens in six games to reach their first finals since 1994.
In the match-up between the last two Stanley Cup champions, the Blackhawks rallied from a 3-1 series deficit but were unable to get over the line on home ice as they sought to become the first team to win back-to-back NHL titles since the Detroit Red Wings in 1998.
"I thought both teams left it out there and unfortunately somebody had to lose," Blackhawks head coach Joel Quenneville told reporters. "A tough ending."
The never-say-die Kings came from behind three times in Sunday's contest to emphasise the battling qualities of a team that has emerged victorious in three consecutive Game Seven deciders in this season's playoffs.
"We never once believed tonight that we weren't going to win this game," said the Kings' Drew Doughty, who leads the playoffs in points (16) for a defenseman. "We knew that we were going to come back."
Marian Gaborik scored his NHL-leading 12th goal of this postseason with 7:17 left in the third period to tie the score at 4-4 and force overtime after Jeff Carter, Justin Williams and Tyler Toffoli had also tallied for the Kings.
"You need everyone when you get to Game Seven," Kings head coach Darryl Sutter added. "There's always guys that score big goals and make big plays but you need everybody in your lineup out there."
The Blackhawks raced to a 2-0 lead in a high-scoring first period on goals from Brandon Saad and team captain Jonathan Toews.
The visitors struck back when a rebound from the Kings's Dustin Brown was swatted out of the air by Carter for his ninth tally of the playoffs, with the goal upheld after an official review.
The Kings made it 2-2 on a Slava Voynov shot that was deflected to Williams, who beat Crawford with a shot from the slot.
The tie lasted only a matter of seconds as Patrick Sharp scored his first of two goals of the night for Chicago, who led 3-2 after a frantic opening period.
Toffoli then tied the game once more in the second period before Sharp added another goal to give the Blackhawks a 4-3 lead heading into the final frame.
The Kings will host Game One of the best-of-seven Stanley Cup Finals on Wednesday.
"Within the past few years, we've tried to earn the respect of the league," Williams said. "LA is not just a place to come play a hockey game and work on your tan."
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