Schwartz also added an assist on a Kevin Shattenkirk tally during a dominating second period that carried the Blues to their first win in four games.
Andy McDonald supplied a goal and an assist and Barret Jackman also found the net for St. Louis, which leapfrogged the idle Columbus Blue Jackets into the eighth and final Western Conference post-season slot.
The Blues' victory came with a price, however, as goaltender Jaroslav Halak left the game with an undisclosed injury in the first period after making five saves.
Brian Elliott relieved and stopped 19-of-20 shots the rest of the way.
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