After Louis Domingue turned away Scott Parse's attempt, Ekman-Larsson beat Martin Jones' glove side with a wrist shot for the winner. Kings captain Dustin Brown and Phoenix's Andy Miele each converted in the second round of the shootout.
Ethan Werek opened the scoring at 8:21 of the first period off a feed from Darian Dziurynski. Los Angeles countered on Viatcheslav Voynov's power-play goal early in the second, with Brown and Mike Richards drawing assists.
Justin Pogge started in net for Phoenix and stopped 27 of 28 shots before being replaced to begin the third.
Jonathan Quick, the Kings' No. 1 goaltender, allowed a goal on 13 shots in 40 minutes.