Los Angeles won Game 1 in overtime as well, topping the Rangers 3-2 on June 4.
Ryan McDonagh and Mats Zuccarello gave New York a 2-0 lead in the first period. Martin St. Louis and Derick Brassard also scored, while Henrik Lundqvist made 39 saves.
Marian Gaborik scored 7:36 into the third period to tie the game 4-4 for the Kings. Jarret Stoll, Willie Mitchell and Dwight King also scored for Los Angeles.
Jonathan Quick stopped 34 shots for the Kings.