Alec Martinez also scored for the Kings, who opened their first playoff series against their local rivals with two victories at a road arena packed with their own fans.
Dwight King added an empty-net goal for Los Angeles, which has won six straight post-season games and is halfway to its third straight trip to the Western Conference finals.
Patrick Maroon scored a power-play goal and Jonas Hiller stopped 14 shots for the Ducks, who couldn't crack the Kings' NHL-best defence despite controlling play for long stretches.
Game 3 is Thursday at Staples Center.
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