Manuel Locatelli was the Azzurri’s hero with a goal in each half, to score the first brace of his career, before Ciro Immobile scored a third in the capital just before the end of normal time.
After beginning the competition with a dominant 3-0 victory over Turkey on the opening day, Wales’ 2-0 defeat of the same opponents shortly before kick-off, gave Italy the chance to progress with one game to spare.
With Switzerland willing to defend deep in their own half and attempt to hit Italy on the counter-attack, the Azzurri took control of the game and looked determined not to be frustrated.
However, all Roberto Mancini’s side had to show for dominating possession, was an Immobile header just over the crossbar and a wild shot from distance by Lorenzo Insigne.
On 19 minutes it looked as though Italy had taken the lead, Giorgio Chiellini rose at a corner kick with two Swiss players and, when the ball landed kindly at the feet of the Juventus man, shot past Yann Sommer.
VAR quickly halted the partying home fans, though, by spotting an accidental handball as the defender challenged in the air and, to make matters worse, Chiellini withdrew almost immediately for Francesco Acerbi. Seemingly injuring his hamstring, wheeling away in celebration.
Italy’s misfortune was soon forgotten, though, when a wonderful first-time pass from Locatelli found Domenico Berardi on the right flank and, after dribbling to the byline, rolled the ball across for the onrushing Sassuolo midfielder to sweep the ball home.
Having won their previous nine international matches without conceding a goal, Italy could have been forgiven had they simply defended their advantage, but had doubled their lead within six minutes of the restart.
Locatelli found himself unmarked 20 yards from the Switzerland goal and, with plenty of time and space to control a Nicolo Barella pass, hit a powerful low left-foot strike into the bottom corner.
The Italians did then conserve some energy for the challenges to come, but eventually added another on 89 minutes when Immobile struck a similar effort from distance.
Although qualification for the knockout stages is guaranteed, the Azzurri now face Wales on Sunday afternoon, in a fixture that becomes a play-off to decide who will top Group A.