Alec Martinez and Anze Kopitar scored in the second period, before Jeff Carter and Justin Williams added power-play goals in the third.
Los Angeles were also grateful to Jonathan Quick, who made 22 saves for his third post-season shut-out, a Kings record.
The Kings were the eighth-seeded team from the West heading into the play-offs and had just the 13th best record overall.
So far in post-season play they have won 15 games and lost just two.
They will try to wrap things up when they again have home advantage in game four on Wednesday.