Finland needed a win of any kind to progress, but Roared on by the home crowd, Switzerland began as if it was they who had to chase the victory.
Yet they only tested Anna Koivunen via a deflected Sydney Schertenleib strike from range in the 13th minute, after Viola Calligaris had failed to execute an acrobatic effort.
Having soaked up a lot of pressure in the opening quarter in the game, the Boreal Owls came close to breaking the deadlock with their first effort of the match.
A deep Evelina Summanen corner found an unmarked Oona Sevenius at the back post and goalkeeper Livia Peng did just enough to keep it out, before a follow-up effort from Katariina Kosola was blocked.
Finland did enough to take a clean sheet into the break, but they very nearly took the lead in stoppage time.
Again they relied on Summanen's delivery - she whipped in a dangerous free-kick from the left which caused havoc in the Swiss box, and though Eva Nystrom didn't know much about it, she diverted the ball towards the bottom corner, but Peng managed to claw it away.
Tensions began to ramp up in the second half, as neither side mustered a shot of any description until after the hour mark. When a strike did finally come, it was courtesy of Switzerland's Smilla Vallotto, but it was side-footed straight at Koivunen.
But inside the final 15 minutes, Marko Saloranta's side were presented with a golden opportunity when a reckless challenge by Calligaris on Emma Koivisto gave referee Stéphanie Frappart no choice but to point to the penalty spot.
Natalia Kuikka was made to wait an age to take the spot-kick, but she held her nerve and rolled the ball down the middle to give Finland a precious lead.
La Nati threw everything at the Finns late on in search of an equaliser, but it looked like they would come up short as a header in the 90th minute from Ana-Maria Crnogorcevic went wide, and an Alisha Lehmann effort was held by Koivunen.
But in the second minute of added time, the Swiss worked the ball well on the right wing, before Joanna Tynnila played a low cross to substitute Riola Xhemaili, who guided the ball home.
In the dying moments, it was Finland's turn to throw the kitchen sink at their opponents, but they could not find a way to turn the match on its head again.
Switzerland avoid becoming the first EURO hosts to be knocked out in the group stage since England in 2005, and they will now play in Bern next Friday against either Spain or Italy.
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