The breakthrough came in the 37th minute, with Freuler turning a low Vargas cross into the back of the net, before the latter fired one into the top corner early in the second period.
Switzerland have advanced to the final eight of the competition and will take on the winner of England's game against Slovakia for the right to feature in the semi-finals.
Here, Sports Mole takes a close look at the last-16 contest, including highlights, our man of the match and the best statistics from what was a deserved win for A-Team.
HIGHLIGHTS
24th min: The first chance of the match comes for Switzerland, as Breel Embolo beats the offside trap before breaking into the Italy box, but the striker's effort is saved by Italy goalkeeper Gianluigi Donnarumma.
26th min: Italy's first opportunity comes for Federico Chiesa, but Switzerland defender Manuel Akanji is on hand to make an excellent block.
32nd min: Ricardo Rodriguez tries his luck from distance, but the Switzerland defender's effort was always rising over the Italy crossbar.
37th min: GOAL! SWITZERLAND 1-0 ITALY (FREULER)
Switzerland make the breakthrough in the 37th minute of the match, as Freuler collects a cross from Vargas before firing the ball into the bottom corner past Donnarumma.
45th min: Donnarumma has to fly across his goal to keep out a clever free kick from Fabian Rieder, as Switzerland threaten to score a second just before the interval.
HALF TIME: SWITZERLAND 1-0 ITALY
46th min: GOAL! SWITZERLAND 2-0 ITALY (VARGAS)
Switzerland double their lead shortly into the second period, as Vargas strikes one from distance, with Donnarumma unable to prevent it from nestling into the back of the net.
52nd min: Almost a bizarre own goal from Fabian Schar, with the Switzerland defender, who was under no pressure, turning against his own post with a header.
73rd min: Italy have a rare venture forward, but it is a comfortable save for Yann Sommer, as the Switzerland goalkeeper keeps out a strike from Mateo Retegui.
74th min: Italy come close to registering, but Gianluca Scamacca turns against the post from close range, with Switzerland surviving a dangerous moment.
FULL TIME: SWITZERLAND 2-0 ITALY
MAN OF THE MATCH - MANUEL AKANJI
Granit Xhaka was excellent in the middle of the Swiss midfield, while Freuler and Vargas are certainly worth a mention in this particular category.
It was a real team performance from Switzerland, but the star man was Manchester City's Akanji, with the centre-back putting in an excellent display to help his side keep a clean sheet.
Akanji was defensively brilliant, but he was also excellent in possession of the ball and often calmed his side down during difficult periods, especially in the second half; it was one of the best defensive performances from any player at the competition this summer.
STANDOUT MOMENT
Vargas's strike was excellent, and it came at such a crucial period of the match.
There did not appear to be too much on when the attacker settled just inside the Italy box, but he was able to place one into the far corner for one of the goals of the tournament.
Donnarumma has been one of the best goalkeepers at the competition, and the fact that Italy's giant stopper was unable to get anywhere near it is an indication of the impressiveness of the strike.
BEST STATS
MATCH STATS
Possession: Switzerland 48%-52% Italy
Shots: Switzerland 16-9 Italy
Shots on target: Switzerland 4-1 Italy
Corners: Switzerland 4-6 Italy
Fouls: Switzerland 9-15 Italy
LINEUPS
SWITZERLAND (3-4-3): Sommer; Schar, Akanji, Rodriguez; Aebischer (Steffen 92'), Freuler, Xhaka, Rieder (Stergiou 72'); Vargas (Zuber 71'), Embolo (Duah 77'), Ndoye (Sierro 77')
ITALY (4-3-3): Donnarumma; Di Lorenzo, Mancini, Bastoni, Darmian (Cambiaso 75'); Cristante (Pellegrini 75'), Fagioli (Frattesi 86'), Barella (Retegui 64'); Chiesa, Scamacca, El Shaarawy (Zaccagni 46')