They are unbeaten in Russian Federation, have scored in every game and a defeat against Portugal last October is the only blemish in an impressive run of results over the past two years.
The Swedes took the lead in the 66th minute at St. Petersburg when Emil Forsberg's right-foot shot deflected off defender Manuel Akanji and past the wrong-footed Yann Sommer. Add to that a bit of Forsberg stardust, and the Swedes can dare to dream, just like they did against Switzerland.
Forsberg had to clear a header from his goal line after Breel Embolo met a corner in the 79th minute and then, ten minutes later, Switzerland moved upfield after Toivonen's error and another header, this time from Haris Seferovic, brought a low save from Robin Olsen.
Switzerland had more possession, but couldn't find a spark of inspiration to unlock the Swedish defense.
England finally ended their penalties curse when they beat Colombia 4-3 in a penalty shootout after their World Cup last-16 clash ended in a 1-all draw with the South Americans finding an equaliser in the 93rd minute.
At the other end Granit Xhaka hammered one shot narrowly over before Blerim Dzemaili followed suit.
On seeding, defending champions Germany would have expected to be in Samara on Saturday but they finished bottom of Group F in Russian Federation, an ignominious exit that would have come sooner had Sweden held out for a few seconds more to draw their clash in Sochi.
"There was something missing in that match", Switzerland coach Vladimir Petkovic said.
The Swiss shook off the cagey start to drastically improve their team play and positioning, but they had only themselves to blame for wayward crosses and shots as displayed by Xhaka and Shaqiri.
This was only Switzerland's fourth defeat in their last 15 matches at the last four World Cup tournaments, with three of those defeats coming by a 1-0 scoreline. We clearly wanted to do more.
"It means so much for me, I'm just so happy in particular for the team that we managed to win again in an extraordinary way", Forsberg told the media afterwards.
But, perhaps a sign of nerves, they were both hugely wasteful as the Swede's and Swiss looked to secure their first World Cup quarter-finals since 1994 and 1954 respectively. "Over the past matches that I've seen with the Swedish team, all the opponents have had a hard time developing those emotions when they were on the pitch against them". "We played out of defence too slowly and we also tried to play diagonal passes, but we were not good enough".
Manager Janne Andersson has few star names in his squad but has built a well-organised team who defend well, are hard-working and have a strong team ethic.
"We know that we're a good team, we've earned our successes".
"We're going to focus on one thing when we've digested this victory, and that's the game on Saturday". It's all about the process right now and it's full steam ahead for us.
"We're massively disappointed. That's a really bitter pill", Sommer said.
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