The home team got off to a shock start and went up 2–0 before the match clock showed four minutes.
Attilio Biasca scored the opening goal after 40 seconds, and Ken Jäger gave the Swiss a two-goal lead at 3:59.
But the Finns stopped the bleeding, worked their way into the game, and after two periods Aleksander Barkov had both reduced the deficit and equalized.
Jäger's winning goal came in a five-on-four situation, and with 55 seconds left Switzerland increased the lead to 4–2 with an empty-net goal.
The quarter-final Switzerland–Sweden will be played in Zurich at 8:20 p.m. on Thursday.
Other quarterfinals: Canada–USA, Finland–Czech Republic, Latvia–Norway.
