Remo Freuler and Ruben Vargas scored the goals for Switzerland, and Italy were unable to find a response on a hugely disappointing night for the reigning European champions.
Here, Sports Mole takes a close look at how each player performed during the last-16 fixture.
Switzerland player ratings vs. Italy: Akanji puts in man-of-the-match performance
GOALKEEPER
Yann Sommer - 7/10
Did not have much to do in terms of saves, with Italy managing just one shot on target, but he was calm and composed, while his use of the ball was also hugely impressive.
DEFENCE
Fabian Schar - 8/10
One of Switzerland's best players on the evening. Almost scored a bizarre own goal in the second period, but even that would not have taken away from his excellent defensive performance.
Manuel Akanji - 9/10
Switzerland's man-of-the-match against the Italians. The Manchester City defender was rock solid in the middle of the back three, while he was also calm and composed in possession of the ball.
Ricardo Rodriguez - 8/10
Another who deserves huge respect for his performance on Saturday evening. Will not grab any headlines on Sunday morning, but he used his experience to make it difficult for Italy.
MIDFIELD
Michel Aebischer - 7/10
Full of running in the right-sided wing-back position and prevented Italy from gaining any sort of joy down that side. A true selfless performance from the 27-year-old.
Remo Freuler - 8/10
Made the breakthrough with a composed finish shortly before the interval, and he was excellent alongside Granit Xhaka in the middle of the Switzerland midfield.
Granit Xhaka - 8/10
Ran Akanji close in terms of the man-of-the-match award on Saturday night. The ex-Arsenal man is having an excellent tournament, and he contributed heavily to Switzerland's win against Italy.
Fabian Rieder - 7/10
Came close to scoring with a clever free kick in the first half and proved to be an energetic presence for Switzerland before being replaced in the 72nd minute of the contest.
ATTACK
Ruben Vargas - 8/10
Set up Freuler for the opening goal of the match before finding the back of the net with a brilliant strike early in the second period. One of Switzerland's best players against the Italians.
Breel Embolo - 7/10
Not a headline-grabbing performance from Embolo, but he occupied the Italian defence and showed some excellent hold-up play, especially in the opening 45 minutes of action.
Dan Ndoye - 7/10
Not difficult to see why he is interesting major clubs this summer, including Manchester United. A real threat during his 77 minutes on the field, with Italy struggling to deal with his power.
SUBSTITUTES
Leonidas Stergiou - 6/10
The inexperienced defender was trusted of the bench on Saturday, and he was able to pick up the pace of the match with ease to help Switzerland see out the result.
Steven Zuber - 6/10
No surprise that he settled into the contest due to his experience at international level, and like Stergiou, he played a role in Switzerland keeping out Italy in the latter stages.
Kwadwo Duah - 6/10
Proved to be the perfect impact substitute for Switzerland, as his pace and direct running caused a tired Italy defence real issues in the final stages of the fixture.
Vincent Sierro - 6/10
Was given the final 13 minutes as a replacement for the brilliant Ndoye, and like his fellow substitutes, he played a role in helping Switzerland see out the last-16 contest.
Renato Steffan- N/A
Was introduced in the second minute of added time at the end of the 90.
Italy player ratings vs. Switzerland: Scamacca struggles for the Blues
GOALKEEPER
Gianluigi Donnarumma - 7/10
Could do nothing with either of Switzerland's goals, and he made some smart saves during the contest. Donnarumma can be pleased with his overall level at the European Championship.
DEFENCE
Giovanni Di Lorenzo - 5/10
Found it incredibly difficult, especially in the first half, as Switzerland continued to enjoy space in the wide positions. Not a match that the defender will remember too fondly.
Gianluca Mancini - 6/10
Managed to hold firm under some pressure in the early stages, but he picked up a yellow card just before the hour and did not receive too much protection from those ahead of him.
Alessandro Bastoni - 6/10
Arguably Italy's best defensive performer, but it still only earns him a 6/10. Bastoni did manage to win some individual battles, but it was a difficult night against a Switzerland side full of movement.
Matteo Darmian - 6/10
Will not remember the match too fondly. Struggled against Switzerland's impressive forward players, and he was replaced in the second half, as Italy chased the match.
MIDFIELD
Bryan Cristante - 6/10
Was unable to make his mark in midfield for the Italians, with Switzerland dominating in that area. The midfielder was replaced in the 75th minute of the contest by Lorenzo Pellegrini.
Nicolo Fagioli - 5/10
Switzerland were dominant in the midfield on Saturday, and the game passed Fagioli by for long spells, with the 23-year-old eventually being replaced in the latter stages of the contest.
Nicolo Barella - 6/10
Easily Italy's most talented player, but the midfielder picked up an injury in the early stages of the contest and never appeared to recover. Was substituted in the 64th minute of the match.
ATTACK
Stephan El Shaarway - 6/10
Was replaced at the interval after struggling to make his mark in an opening 45 minutes where Italy were unable to cause Switzerland problems in the final third of the field.
Gianluca Scamacca - 4/10
Hit the post late on when he really should have scored, and it might have been a different outcome had the ball found the back of the net. Had a really difficult evening as Italy's centre-forward.
Federico Chiesa - 6/10
Proved to be a threat in the first period when Italy were able to isolate him with a Switzerland defender, but the Juventus attacker faded as the fixture developed.
SUBSTITUTES
Mattia Zaccagni - 6/10
Entered at the half-time break, with El Shaarawy removed, but the forward was unable to help change Italy's fortunes, with Switzerland's defence coming out on top.
Mateo Retegui- 6/10
Replaced Barella in the 64th minute of the contest, and he showed some nice touches, but he came into a struggling side and was unable to oversee a change.
Andrea Cambiaso - 6/10
Juventus defender replaced Darmian in the 74th minute of the contest, and he was able to help Italy tighten up in the final 15 minutes of the last-16 fixture.
Lorenzo Pellegrini - 6/10
Only given the final 15 minutes to make an impact, and it was a huge ask at that stage of proceedings. Like a number of his teammates, was unable to really make a telling contribution.
Davide Frattesi - 6/10
Was introduced in the 86th minute of the fixture, with Frattesti therefore hardly given the chance to help his side stage a late recovery against an impressive Switzerland outfit.