Emil Forsberg's shot from the edge of the penalty area was poorly struck and was heading straight for Swiss goalkeeper Yann Sommer only for his central defender Manuel Akanji to deflect it high in to the top corner.
Seconds later, Switzerland were down to 10 men - an irrelevance given the time on the clock - when Michael Lang pushed Martin Olsson as he was clean through.
Referee Damir Skomina had initially pointed to the spot, but after reviewing the incident with VAR decided that the contact was outside of the area and overturned his decision to instead award a free-kick.
The match would end immediately afterwards to put the Swedes in place for a quarter-final clash with the victor of England/Colombia later on Tuesday.
The Swedes last made it to this stage of the competition in 1994, when Tommy Svensson's side finished third in the United States.
Even before his goal, Forsberg looked the most likely player to make an impact as Swiss duo Xherdan Shaqiri and Granit Xhaka failed to shine in a bizarrely passive performance from the side ranked sixth in the world and given the chance to reach the quarter-finals for the first time since 1954, when they were the host nation. Either Colombia or England will await them in the quarter-final.
"We have managed to bring together different cultures, different talents, different ideologies and they help us to play really good football", Petkovic told Eurosport.
In fact, they could have been 2-0 down in the first ten minutes if Marcus Berg and Albin Ekdal had been more clinical.
And when at the end the Swiss pressed for an equaliser, Forsberg cleared from close to his goal and several team-mates put in desperate blocks as they showed that they will provide a hard test for anyone who wants to stop them reaching the final.
Zuber, however, set up Switzerland's best chance of the half, laying the ball on a plate for Blerim Dzemaili who hammered a shot over from inside the box.
"We have a clear plan in place for what we're going to do, but I'm not going to enter into any more details".
Xherdan Shaqiri looked to pull the strings for Switzerland and he imposed himself on the game early by delivering unsafe balls for Blerim Dzemaili and Josip Drmic, but neither could make the majority.
The match was far from this month's best, destined not to be remembered amid an incredibly memorable World Cup, but Sweden will not care one iota.
Haris Seferovic - Joined Drmic up front in the final 15 minutes and tested Robin Olsen with a header.
Switzerland also came very close.
"We're so focused on what we're doing right now that I don't think I'm taking any of this in".
"We've been very fortunate so far, that is true, but what we've seen throughout the tournament is that in spells we have been playing very well", Petkovic said on the eve of the match.
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