The Blackhawks have piled up 18 out of a possible 24 points at home this season and had to fight off a New York team that was trying to win its third in a row. That would have equaled the Islanders' longest such streak of the season.
Toews scored shorthanded late in the second period to give the Blackhawks a 3-2 lead.
P.A. Parenteau tied it for the Islanders 46 seconds deep in the third with a power-play goal. Patrick Sharp put Chicago back in front 5:08 into the third, but the Islanders tied it again on the first goal of the season for Nino Niederreiter.
The shootout goal by Toews came in the second round against Al Montoya, who stopped 30 shots in regulation and overtime.
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