Two teams boasting nearly identical formations matched each other to a tee in yet another lukewarm first half, which the Three Lions maybe just shaded, but neither goalkeeper faced a shot on target before the break.
The first quarter-final of the day belatedly began to open up a bit more in the second 45, where a well-worked Breel Embolo opener preceded a stunning equaliser from Bukayo Saka, as England were bailed out by yet another moment of magic.
The Arsenal man's peach of a strike saw England go to extra time for the second match running, where Liverpool cult hero Xherdan Shaqiri nearly sealed victory for the Swiss with an outrageous corner, which struck the upright and bounced away.
While all five of Gareth Southgate's penalty takers dispatched their spot kicks, Manuel Akanji's weak attempt was comfortably kept out by Jordan Pickford, as England banished their penalty demons from Euro 2020 but still left plenty of concerns lingering about their overall display.
Scintillating Saka saves England's bacon
Even before his wonderful equaliser - which had shades of his wonder goal for Arsenal against Manchester United in January 2023 - Saka was already one of England's principle threats in the first half, giving Michael Aebischer a rotten time of things.
The 22-year-old dribbled past his Swiss counterpart four times in the first half - the most of any player at the Euros so far - and Yakin's side quickly learned their lesson after dropping off the Hale End graduate 10 minutes from the end.
Cutting inside from the left, 20 yards from goal and under no pressure whatsoever, Saka wrapped his foot around the ball, and Yann Sommer could only helplessly watch the Arsenal man's delicious curler kiss the inside of the post and spark beer-throwing bedlam from the England end.
Akanji apoplectic as Pickford guesses right
Choosing two centre-backs to take your first two penalties is a particularly plucky move, and in truth, Manuel Akanji did not look like he was ever going to score with his opening effort.
The Manchester City man - who was actually a strong performer during the 120 minutes - went for an Ivan Toney-esque short run-up, but there was no fooling Pickford, who only had to shift slightly to his left to keep out Akanji's strike.
The Switzerland defender let out an almighty roar of frustration as the England fans behind Pickford's goal exploded into delirium, and while three of his compatriots stayed perfect from the spot, England's penalty panache was just too powerful.
"Pressure is for tyres" as England demonstrate spot-kick supremacy
Laughter-inducing words spoken by Alan Shearer after Trent Alexander-Arnold dispatched the fifth of five perfect England penalties, marking just the second time that the Three Lions have ever registered a 100% success rate in a major tournament shootout, and the first since 1996.
Alarm bells may have been ringing when Harry Kane was taken off after a collision with Southgate and a water cooler, but Three Lions fans need not have worried, as the composure exhibited from their five takers was totally uncharacteristic of England teams gone by.
Saka exorcised his 2021 demons, Toney did what Toney does, Cole Palmer - you know the rest - Bellingham lived for the pressure, and finally, Alexander-Arnold, only a late substitute in extra time, punched England's ticket to the last four.
Amid the penalty euphoria, though, the first 80 minutes saw another meek performance from Southgate's men, who barring Saka were often devoid of attacking ideas, and this is now a fourth match on the spin where England have not come up trumps in 90 minutes.
What next for England and Switzerland?
As Southgate and co somehow try to control their emotions and revert to a composed state, they will learn their semi-final opponents in just a matter of hours, as Turkey and the Netherlands fight for the right to meet the Three Lions in the last four.
As for a heartbroken Rossocrociati side, who have still never reached the final four of a major tournament, the immediate concern is that of Yakin's future, as the head coach's contract curiously only runs until the date of the Euro 2024 final - July 14.
Whoever is in charge will be navigating Switzerland through a daunting Nations League section, as Spain, Serbia and Denmark await in League A Group 4, which begins in September.