Murray's goal broke a 2-2 tie, Rick Nash's power play goal doubled the advantage with less than 4 minutes to go and Fedor Tyutin added an insurance tally for Columbus, which posted its first regulation win over the Blues in four years.
Steve Mason turned aside 19-of-21 shots for Columbus.
Eric Brewer and Patrik Berglund scored 1:23 apart in the first period to give St. Louis a short-lived 2-0 lead and Jaroslav Halak made 25 saves as the Blues lost for the eighth time in 10 games.
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