Kevin Shattenkirk added another goal on the man advantage before the end of the first, and Jori Lehtera and Kyle Brodziak added short-handed scores in each of the next two frames.
Lehtera had a goal and an assist in his preseason debut after having right ankle surgery Aug. 4.Dennis Rasmussen and Brandon Mashinter scored first-period goals for Chicago (3-2).
Dmitrij Jaskin opened the scoring when he beat Viktor Svedberg to a lose puck off a faceoff outside of the offensive zone, and sent a wrister pass Scott Darling at 3:20 in the first. Rasmussen evened the scoring 14 seconds later with a tap in off his own rebound. Mashinter gave the Hawks a lead off a feed from Viktor Tikonov behind the net at 4:55 in the first.
Chicago was without their top scorers as Bryan Bickell was the top returning scorer on the ice.
The Hawks went 0-for-7 on the power plays and 0-for-2 on the penalty kill. Darling played the entire game, stopping 19 shots. Jake Allen made 20 saves for the Blues, who close their preseason 4-2.
Chicago plays their final preseason game at home against the Dallas Stars on Saturday.