Dustin Brown was the hero for the hosts, scoring midway through the second additional period in Los Angeles as the Kings came from two goals down to take a commanding 2-0 series lead on Saturday.
Brown deflected Wilie Mitchell’s effort past a helpless Henrik Lundqvist, who finished with 40 saves, for his fifth goal of the play-offs.
It is the second consecutive game a clash between the two teams has been decided in overtime, after the Kings prevailed 3-2 on Wednesday.
Game three is in New York on Monday.
Just as the Rangers did in game one, they raced out to a 2-0 lead in the first period, only to squander it.
New York’s Dominic Moore intercepted Justin Williams in the defensive zone and passed the puck to Ryan McDonagh, who found the back of the net in the 10th minute of the opening stanza.
The Rangers were the beneficiaries of yet another turnover as they doubled their advantage eight minutes later.
McDonagh was in the thick of the action, firing his shot towards Kings goalkeeper Jonathan Quick before Mats Zuccarello tapped it into the net.
The Kings hit back early in the second period through Jarrett Stoll but the Rangers restored their two-goal advantage thanks to Martin St Louis on a power play.
Los Angeles reduced the deficit again three minutes later, with Mitchell making the most of a power play only for Derick Brassard to put New York 4-2 ahead at the start of the third.
However, two unanswered goals in the third period from Dwight King and Marian Gaborik sent the game into overtime.
After a goalless 20-minute period, the Kings finally made the breakthrough as the Rangers were left ruing another wasted opportunity.
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