A brace from Manuel Locatelli before a superb goal from Ciro Immobile sealed all three points for the Azzurri once again. They will face the runners-up of Group C in the next round if they avoid defeat in the last match.
Roberto Mancini's side were dealt an early blow when skipper Giorgio Chiellini went off with a hamstring problem. But all fears were allayed just minutes later when Locatelli tapped home a cross from Domenico Berardi just before the half-hour mark.
The home side resumed the match after the break in similarly dominant fashion and found themselves two for good. The Sassuolo talisman popped up with another strike, a brilliant effort from distance.
The Swiss, who had failed to beat Italy's stoic defense until then, came really close a few times. But some last-ditch tackles and near-misses kept them from clawing their way back into the match.
Ciro Immobile then made sure all their hopes of a late comeback were quashed with a fantastic long-range volley in the penultimate minute of normal time to put the match beyond doubt.
Italy will play their final group fixture against Wales on Sunday while Switzerland face a must-win clash against Turkey on the same day. Here are the major talking points from the Rome encounter:
#1 Manuel Locatelli stars for Italy
Of all the star players starting for Italy tonight, Manuel Locatelli stole the show with his unexpected double. His goals helped the hosts secure another victory and qualify for the last-16 too. The youngster, who had scored just once for the Azzurri before in 11 games, demonstrated his deadly finishing abilities.
Locatelli broke the deadlock with a simple tap-in after some good work down the flanks by Domenico Berardi. He sneakily ran in behind the Swiss defense and smashed his club-mate's cross from close range. He rounded off his brace with a spectacular effort from about 25-yards out in the second-half.
Manuel Locatelli, remember the name!
#2 Giorgio Chiellini went off injured
Albeit nothing serious, Giorgio Chiellini was subbed just 24 minutes into the match after he pulled a hamstring. It was undoubtedly a big loss for the Azzurri, though his replacement Francesco Acerbi cemented the void with elan. Chiellini will now be examined ahead of their final group fixture against Wales on Saturday.
After tonight's victory, Italy have already qualified for the last-16 as group winners. Roberto Mancini's side are mathematically unassailable for the other three sides. So Chiellini's services won't be needed for their last pre-knockout match and might as well be rested.