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.
Wisconsin business offering 'therapeutic cuddling' forced to close
Video of Victoria’s Secret models trying to 'twerk' hits Instagram