The Canadian win seemed virtually safe when the hosts led 4-0 late in the third period before Esa Lindell gave the visitors a very thin lifeline by finally getting on the scoreboard for the Finns with 6:41 remaining on the clock.
Mikael Granlund, who scored Finlands winner in the overtime-drama against Sweden, then scored twice 23 seconds apart to cut the lead to one with 1:17 left on the clock.
But Sidney Crosby then crushed all Finnish hope of what would have been an epic comeback when he scored into the empty net, to finally get his first goal of the tournament, with under a minute remaining of the match.
Until the late drama Canada had seemed well in control of proceedings as they scored two goals in quick succession in the first five minutes of the game. First Connor McDavid beat Kevin Lankinen using a screen before Nathan MacKinnon doubled the lead just 46 seconds later.
Brayden Point then reacted quick to score Canada's third on a rebound later in the first period. MacKinnon then scored his second of the evening just over five minutes into the second period, when he launched a one-timer into the back of the net following a great assist by Crosby.
Sweden can match Canada on five points with a regulation win tonight against the U.S but the host nation have already secured their place in the final thanks to their win over the Swedes in the opening game of the tournament.