Corey Crawford made 31 saves for the Blackhawks, who were coming off a shootout win at home against Pittsburgh on Sunday. They have won three of four overall.
With the victory, Chicago created a five-team logjam between the seventh and 11th spots in the Western Conference standings. St. Louis has 63 points, five fewer than the Blackhawks.
Andy McDonald and Brad Boyes had given the Blues a 2-0 lead in the opening frame, while Alex Pietrangelo drew St. Louis within a goal in the third period.
Ben Bishop, making his first start of the season for the Blues, was pulled in the second after allowing four goals on 18 shots. Ty Conklin stopped seven shots in relief.