Crawford turned aside all 11 shots he faced in the second period as the Blackhawks scratched out a 1-0 lead on a goal by Bryan Bickell 4 1/2 minutes into the frame.
The Blackhawks doubled their advantage early in the third when Hossa scored following a face-off in the St. Louis zone even as Chicago had Marcus Kruger in the penalty box.
Jonathan Toews assisted on the insurance goal as the NHL-leading Blackhawks improved to 32-5-4 (88 points).
Brian Elliott made 24 saves the Blues, who hold the sixth seed in the Western Conference standings.
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