Bernier turned aside all 26 shots he saw for Los Angeles, which pulled into a tie with Dallas and Colorado for the Western Conference's eighth and final playoff spot with 70 points.
Justin Williams, Dwight King and Anze Kopitar each scored in the first period and the Kings never looked back.
Kopitar and Williams added assists and Jordan Nolan also scored for Los Angeles.
Niklas Backstrom let in four goals on only 15 shots for the Wild, who have gone 3-2 in their last five games and remained five points out of a playoff slot in the West.
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