Both were recalled from the minors prior to Saturday's 2-1 overtime loss to the New York Islanders, taking the lineup spots of Jarret Stoll and Dustin Penner.
King, a forward and fourth-round 2007 Los Angeles draft choice, opened the game's scoring with a tally midway through the first period. Nolan -- a center who was a seventh-round 2009 pick -- scored with 11:29 left in the third for 3-2 Kings lead.
Andrei Loktionov also tallied and Justin Williams added an empty-netter for Los Angeles, which wrapped up a six-game road trip with a 2-3-1 mark.
Jonathan Quick earned the victory with 26 saves.
Kari Lehtonen turned aside 12-of-15 shots for the losers.