The Blues have won three in a row after a three-game skid. St. Louis entered the night in eighth place in the Western Conference.
St. Louis has won all three meetings with Columbus this season and 10 of 11 overall. The Blue Jackets failed to earn a point for only the third time in 19 games.
Backes, who broke a 15-game goal-scoring drought in Chicago on Thursday, has nearly doubled his goal total in two days. He has five goals this season.