Toews ran his goal total this season to 25 in boosting Chicago to a 4-1 advantage heading into the final 20 minutes.
Jarome Iginla had a goal and two assists for Calgary, scoring his 28th of the season midway through the third to bring the Flames within 4-3.
Corey Crawford got the victory with 21 saves.
Miikka Kiprusoff was removed from the game after giving up four goals on 19 shots. Henrik Karlsson made nine saves in the third period.
Calgary was coming off a home-and-home sweep of St. Louis.
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