Kopitar's fifth and sixth goals of the season staked the Kings to a lead they wouldn't surrender. He also added an assist.
Dustin Brown and Drew Doughty each notched a goal and an assist for Los Angeles, which continued its best start at home since 1980-81, raising its record to 8-0-0 at Staples Center.
Rob Schremp scored and Dwayne Roloson turned aside 29-of-34 shots in the Islanders' loss.
Trader Joe's: Car crashes into Long Island store, injuring 11
Selena Gomez drops F-bomb, walks off stage during Jingle Ball performance