Steen broke the deadlock with his ninth goal of the season and David Backes added an empty-net tally with 59 seconds remaining.
Vladimir Sobotka and Backes both had a goal and two assists, helping the Blues halt a two-game skid.
Ty Conklin saved all 12 shots he faced in the third period and stopped a total of 25 shots.
Jonathan Quick made 25 saves for the Kings, who have split the first two outings of a five-game road trip.
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