Remo Freuler made the breakthrough in the 37th minute of the contest, before Ruben Vargas doubled Switzerland's advantage early in the second period of the round-of-16 fixture.
Italy were second-best throughout the contest, with the Swiss fully deserving of their spot in the quarter-finals, which will be against either England or Slovakia, with the pair clashing on Sunday evening.
Switzerland reached the final eight of Euro 2020, which proved to be their best-ever showing at a European Championship, but they look capable of being dark horses for the trophy this summer.
As for Italy, the Euro 2020 holders have been dumped out, and having failed to impress in the group stage of the competition, it will go down as a hugely disappointing tournament for the Blues.
Switzerland's second seriously harmed Italy
After a poor opening 45 minutes, Italy would have been looking to start the second period on the front foot, but they found themselves 2-0 behind just 27 seconds into the second 45.
It was a stunning effort from Vargas, who picked out the top corner with a brilliant effort from distance.
Vargas was the provider for the game's opening goal, meanwhile, setting up Freuler to make the breakthrough in the 37th minute, with Italy harmed by efforts either side of the half-time whistle.
Switzerland were the dominant force
The opening 20 minutes of the contest passed without incident; Switzerland were in control of the possession, but they were finding it difficult to carve out openings, while Italy were untidy on the ball.
The Swiss were excellent against Germany in their final group-stage fixture, and Murat Yakin's side were full of confidence against Italy, showcasing their technical ability in midfield and clever movement in the final third.
The first chance of the match came for Switzerland in the 24th minute, as Breel Embolo beat the offside trap before breaking into the Italy box, but the striker's effort was saved by goalkeeper Gianluigi Donnarumma, who has been Italy's standout player at the tournament.
Switzerland made the breakthrough in the 37th minute of the match, as Freuler collected a cross from Vargas before firing the ball into the bottom corner past Donnarumma via a slight deflection, and it was no more than Yakin's team deserved for their dominance during the contest.
The Swiss came close to a second just before the half-time break, with Fabian Rieder firing a clever free kick towards goal, but Donnarumma was on hand to make the save.
Switzerland doubled their lead shortly into the second period, and it was an absolute stunner from Vargas, who picked out the top corner with a rasping strike from outside the Italy box.
Fabian Schar headed against his own crossbar soon after, with Italy almost given a huge slice of luck, but Switzerland survived the dangerous moment, and they were able to keep a clean sheet on Saturday night.
Italy hugely disappointing in last-16 contest
Italy were incredibly poor on Saturday evening, with Luciano Spalletti's side unable to match Switzerland from either a defensive or attacking point of view.
The Blues were champions at Euro 2020, but they have not qualified for either of the last two World Cups and were never fancied to be serious challengers for the crown this summer.
Gianluca Scamacca hit the post from close range late on, and there was a slight hint of a potential comeback from Spalletti's team, but it never looked to be a serious possibility, with the excellent Switzerland fully deserving of their position in the quarter-finals of the tournament.
What next for Switzerland and Italy?
Italy are out of the competition, and once the dust has settled, the Blues will be looking ahead to their new UEFA Nations League campaign, which begins against France on September 6.
As for Switzerland, they will take on either England or Slovakia in the quarter-finals of Euro 2024, with that contest taking place on July 6.