The Blues opened the scoring at 2:34 of the first as a puck bounced off the end boards off a Blues dump in and popped out directly to Mackenzie MacEachern in front, who beat Corey Crawford on the glove side for a 1-0 lead.
Shortly after, the Blues drew their first power play of the night and needed just 14 seconds to convert as an Alex Pietrangelo shot from the point was deflected by Jaden Schwartz in front and into the net for a 2-0 lead at 14:22 of the opening frame.
Brayden Schenn was the beneficiary of another bounce in the Blackhawks end, as a pass from Nathan Walker deflected off Alex DeBrincat's stick and right to Schenn at the bottom of the circle, where he ripped a half-slapper past Crawford for a 3-0 lead at 8:56 of the third.
As Chicago was looking for a late goal, an Olli Maatta pass errantly went right to Tyler Bozak, who took a quick slap shot from inside the blue line for a 4-0 lead at 18:11 of the final frame.