Scrivens yielded the tiebreaker goals after taking the net during a scoreless overtime to replace Jonathan Quick, who exited with a groin injury.
Cody Hodgson scored twice in regulation as the last-place Sabres improved to 1-8-1 on their home ice.
Ryan Miller made 43 saves.
Dwight King and Justin Williams scored for the Kings and Quick made 15 saves before his injury.
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