Davis Drewiske and Jarret Stoll also scored for the Kings, who halted a two-game losing streak.
Bernier took over in net after Los Angeles gave regular goalie Jonathan Quick a rest and responded by turning aside 21-of-22 shots.
Alex Steen got the only goal for struggling St. Louis, which dropped its fifth straight.
Brian Elliott managed to record just 19 saves in the Blues' loss.
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