Early on in Tampere, Switzerland did not pose any kind of threat to Finland, as they failed to register a single shot on goal in the first period, though the home side managed just three of their own as defences were very much on top.
The visitors finally forced Harri Sateri into action in the second 20 minutes, but his six saves, plus Reto Berra at the other end taking his total to eight, kept the match goalless through 40 minutes.
But finally, eight minutes into the third period, the deadlock was broken by the away side, as Giancarlo Chanton won possession in the neutral zone and found Fabrice Herzog, who fed Ken Jager on the left, and he had time to pick his spot past Sateri.
Having found the net once, the Swiss had the confidence to score a second a little over three minutes later with a remarkably similar goal - this time Michael Fora and Nicolas Baechler combined in the middle, while Attilio Biasca popped up on the left wing to power the puck home.
With just under three minutes to play, Finland finally had the home crowd on their feet when Mikko Lehtonen and Jere Innala combined for the latter to score on a powerplay.
But hopes of a Leijonat comeback were dashed in the final minute, when Christoph Bertschy stole the puck and raced away to roll it into an empty net, giving Switzerland a 3-1 win.
Despite this being the Finnish leg of the 2025/26 Euro Hockey Tour, Sweden's match with Czech Republic was taking place at Catena Arena in Angelholm, before the pair head to Tampere for the remaining matches.
Sweden made full use of the familiar surroundings, as after a goalless first period in this match, too, the Tre Kronor took the lead in the 14th minute of the second courtesy of Simon Ryfors' first goal for his country.
Ryfors' night got better early in the third as he and Tim Heed combined to set up Marcus Sylvegard to make it 2-0, and though Jakub Lauko responded soon after to keep the Czechs in it, Erik Brannstrom settled matters in the final five minutes to give Sweden a 3-1 win.
Finland will have another chance to get off the mark on Saturday when they face Czech Republic, after Sweden and Switzerland lock horns earlier in the day. The third and final round of matches will be played on Sunday.
Look ahead to the weekend's action in Tampere on Flashscore.