The Blues' Erik Johnson unleashed a slap shot from right point and Boyes got his stick on it in front of the Blackhawks net, redirecting the puck past Marty Turco for a 2-1 lead 3 minutes into the third.
Brad Winchester added an insurance goal and Vladimir Sobotka got an unassisted tally in the first period for St. Louis, which notched its fourth straight win.
Matt D'Agostini notched two assists and Ty Conklin stopped 25-of-26 shots for the Blues.
Jake Dowell got the only Chicago goal and Turco made 40 saves.
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