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.
Millions of Getty images now available for free via embed tool
Aaron Carter is still in love with Hilary Duff