Columbus began the night as one of three teams within three points of Detroit for the final post-season spot in the Western Conference and the Blue Jackets came through with a key victory against a team that had won its previous six games.
St. Louis took the lead just 1:26 into the game on a slap shot from Kevin Shattenkirk and that was the only goal the Blues managed against Sergei Bobrovsky.
Cam Atkinson tied it with 5:28 left in the opening period and Anisimov scored on a tip-in with 5:40 left in the middle stanza to give the Blue Jackets the lead.
Ryan Johansen added a second-period goal and Marian Gaborik provided some insurance 1:29 into the third.
Bobrovski made 28 saves while Jake Allen, making the 14th appearance of his rookie season with the Blues, allowed all four goals on 18 shots.