Jarret Stoll and Ryan Getzlaf traded goals in the third round of the shootout after the first four participants came up empty. After six more skaters were denied, Williams beat Jonas Hiller up high, and Jonathan Quick saved Kurtis Foster's attempt to earn the extra point for Los Angeles.
Mike Richards scored in regulation for the Kings, who finished a 3-1 homestand on a high note. Quick made 23 saves in the victory.
Hiller was solid with 36 saves for Anaheim, which has gone 1-5-3 in its last nine games and will host the Kings on Thursday.