Bernier, who was called up Monday from Manchester of the American Hockey League, stopped 34 shots and snapped the Kings' four-game losing streak.
Los Angeles trails Detroit by one point for the sixth playoff spot in the West.
Sean O'Donnell and Scott Parse accounted for the Los Angeles goals. Parse broke a scoreless tie at 7:50 of the third period and O'Donnell added the insurance goal at 17:59.
Pekka Rinne turned in 29 saves and Nashville outshot the Kings 34-31. Nashville is in fifth place in the West, one point ahead of Detroit and two ahead of Los Angeles.