Nathan MacKinnon broke a 2-2 tie with 36 seconds to play, and Canada will play for hockey supremacy Sunday.
Canada trailed Finland 2-0 early in the second period after a slow start.
Sam Reinhart brought the Canadians within one with a power play goal midway through the second, and Shea Theodore tied it up midway through the third.
Canada will face the winner of semifinal between the United States and Slovakia.
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