Vargas curled a wonderful shot home from the corner of the penalty area just 27 seconds into the second half, having earlier supplied the cross from which Remo Freuler opened the scoring.

If anything, the scoreline flattered Italy, which produced another miserable performance after barely scraping through Group B with a 99th-minute equaliser in its last game against Croatia.

The result means Spain remains the only team to win back-to-back European championships – in 2008 and 2012 – with Luciano Spalletti's first tournament as Azzurri boss ending in disappointment.

Switzerland, meanwhile, will face either England or Slovakia in just its second European championship quarter-final in Dusseldorf next weekend.

Switzerland dominated from the first whistle and should have gone ahead after 24 minutes, Breel Embolo being denied by a one-on-one save from Gianluigi Donnarumma after latching on to Michel Aebischer's lofted pass.

It had its opener after 37 minutes, though, as Freuler's expert run allowed him to take in Vargas's low cross, his first touch sitting up nicely for a volleyed finish which beat Donnarumma at his near post.

Donnarumma prevented Italy from falling further behind before the break, pushing Fabian Rieder's clever free-kick against his post in first-half stoppage-time.

Things got worse for the Azzurri in the first minute of the second period, Nicolo Fagioli carelessly losing possession from kick-off and Vargas curling a fine effort into the top-right corner.

Fabian Schar almost let Spalletti's team back in when he comically headed Fagioli's cross against his right post, and the other upright was struck with 16 minutes remaining.

Gianluca Scamacca could only turn his close-range effort against the woodwork as Italy continued to toil in the final third, and Switzerland almost added further gloss late on as substitute Steven Zuber flashed a low drive across the face of goal and wide.

As the players re-emerged for the second half and Spalletti hooked Stephan El Shaarawy in favour of Mattia Zaccagni – the man who sent Italy to the Round of 16 with his last-gasp equaliser against Croatia – Italy's supporters must have expected an upturn.

The Azzurri registered just one shot in the first half – a Federico Chiesa attempt with an expected goals (xG) value of 0.03. The last time it managed fewer efforts in the first half of a match was in a 2-0 friendly loss to Argentina in March 2018, when it recorded none.

Those Italian hopes were not realised, however, as the Azzurri conceded possession cheaply before watching Vargas bend home for one of the goals of the tournament.

Coming 27 seconds into the second half, Vargas' strike was the second-quickest scored after half-time in a European championships match, after Marcel Coras for Romania versus West Germany in 1984, when he scored after 21 seconds.

Having seen Switzerland dump pre-tournament favourite France out at the same stage of UEFA Euro 2020, also failing to win two head-to-head meetings in 2022 FIFA World Cup qualifying, Italy was surely well aware of its opponent's qualities.

It was second-best in every department as Murat Yakin's team produced a polished display, of which Vargas was the star.

The forward, who plays his club football in Germany with Augsburg, became the first Switzerland player since 1966 to both score and assist in a knockout match at a major tournament.

He is the seventh different player to score for Switzerland at UEFA Euro 2024, its most goalscorers at any major tournament in its history.