The reigning Stanley Cup champions had given up a 2-1 lead early in the third period before two goals in six minutes saw them to the win, squaring the Western Conference finals at 3-3.
Duncan Keith levelled game six at the Staples Center before Patrick Kane struck with a stunning wrist shot in the 17th minute.
Kane scored twice and set up one in a strong display, which included the match-winner.
Blackhawks goaltender Corey Crawford made 26 saves, including a few in an enthralling final 20 seconds, while Jonathan Quick kept out 21 shots.
It means the Kings will need to win a third consecutive game seven in these play-offs to reach the Stanley Cup finals.
Chicago host the deciding game at their United Center home on Sunday.
Dwight King had given the Kings the first-period lead, which they gave up early in the second when Kane and Ben Smith scored.
Drew Doughty levelled for the hosts early in the third before Alec Martinez’s power-play goal had the Kings headed for a meeting with the New York Rangers in the Stanley Cup finals.
Kane’s super pass set up Keith to make it 3-3 before he did it all himself soon after, skating from the right to the left before unleashing past Quick.
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