Despite being outshot 22-11 in regulation, the Predators kept coming up with crucial blocks to stay alive before left wing Sergei Kostitsyn scored the decisive goal in the eighth round of a tense shootout.
Nashville improved to 2-2-3 for the season while the Kings, bidding for a third straight win in front of a sellout crowd of 18,118 at the Staples Center, slipped to 2-2-2.
The home fans had barely settled into their seats before Nashville struck early, Kings goaltender Jonathan Quick being beaten by a blazing long-range snap shot from right wing Brandon Yip after just 58 seconds.
However, Los Angeles made it 1-1 on a powerplay 13 minutes into the first period when captain Dustin Brown, lurking close to the net, scored his first goal of the season with a wrist shot.
After a scoreless second period, both teams upped the tempo in the third with the Kings more dangerous on offense but the deadlock could not be broken.
It was still 1-1 after five minutes of overtime before Kostitsyn's score through Quick's legs sealed the win after centers David Legwand and Craig Smith and left wing Gabriel Bourque had also scored for the Predators in the shootout.
Nashville goaltender Pekka Rinne, who had lost five of his previous six starts against the Kings, made 23 saves and stopped five of eight shootout attempts.