King's seventh goal of the season on a deflected shot by Linden Vey at 15:08 of the second period put Los Angeles ahead 4-0 and on their way to their fourth consecutive win.
Scrivens faced only two shots in the second period and then turned away all but one of a dozen shots Tampa Bay threw at him in the third.
Victor Hedman scored a goal and an assist for Florida. Valtteri Filppula also scored, and Ben Bishop was tagged for five goals on 31 shots.
Notable deaths of 2014 [PHOTOS]
Julius Randle breaks leg during NBA debut