Peter Holland contributed two goals with an assist and Mason Raymond racked up four assists for the Maple Leafs, who broke an eight-game losing streak against Chicago.
Jonathan Bernier earned the victory with 25 saves.
Patrick Kane tallied his 18th and 19th goals of the season for the Blackhawks.
Brandon Saad also scored as Chicago lost for the first time in four games.
Antti Raanta was roughed up for five goals in 25 shots over 40 minutes before being replaced by rookie Kent Simpson, who stopped 5-of-7 shots in his NHL debut.