Just when it looked as though the game was going to be the third game to go to penalties in this World Cup, Di Maria scored late in extra-time to seal Argentina's place in the quarter-finals, where they will take on either Belgium or USA.
Messi and Di Maria were the ones who were involved in the goal and were the side's key attacking threat. Benaglio in goal was in spectacular form as he thwarted almost everything that came his way.
Let us take a look at how each player performed in the player ratings.
Argentina
Sergio Romero: 6.5/10
Didn’t have a particularly busy game but when he was called upon, showed that he was more than ready to step up to the plate.
Pablo Zabaleta: 7.5/10
Was his usual industrious self. Did well to contain the tricky Mehmedi and went forward at every opportunity, providing the side with some much-need width.
Ezequiel Garay: 6/10
Didn’t have a particularly great game going forward or at the back. Missed a good chance from a set-piece while attacking and conceded a free kick late in extra-time, which almost cost his side the game.
Federico Fernández: 6/10
Although he was rarely threatened throughout the game, he didn’t look too comfortable on the ball and made a hash of several easy clearances.
Marcos Rojo: 8/10
Pushed forward at every opportunity and was one of the side’s main attacking outlets throughout the game. Matched up well with Shaqiri and tracked the Swiss attacker’s every move. Will miss the quarter-final with a booking.
Fernando Gago: 7/10
Was the better of the two defensive midfielders. Not only did he do a good job of marshalling the midfield, but also started a couple of decent attacks.
Javier Mascherano: 7/10
Mascherano was his usual busy self as he had a busy game, lunging into tackles, making crucial interceptions and providing a solid platform for the attack.
Angel Di Maria: 8.5/10
He might not have had as good a game as he had against Nigeria, but Di Maria stepped up his game in extra time. Although he was barely given an inch all game by Ricardo Rodriguez, he managed to make a difference in extra time, scoring the match winning goal right at the end of extra-time.
Lionel Messi: 9.5/10 – Man of the Match
Was almost marked out of the game by the Swiss defence, but Messi showed just why he is one of the best attackers in the world, by creating the winning goal for Di Maria. Also had a couple of good efforts saved by Benaglio. After hardly getting a touch in the first half, he was the source of almost all of Argentina’s attacks second half onwards.
Gonzalo Higuain: 5.5/10
In keeping with his performances so far in the World Cup, Higuain had another quiet game. Aside from his header late in the second half which was well saved by Benaglio, Higuain remained anonymous for most of the game.
Ezequiel Lavezzi: 6.5/10
Although he was neat and tidy in possession, Lavezzi had an otherwise uneventful game. Put in a couple of decent crosses which weren’t made utmost use of.
Substitutes:
Rodrigo Palacio: 5.5/10
Came on for Lavezzi with 15 minutes left to go, but failed to make too much of an impact on the game.
Jose Maria Basanta: NA
Came on in extra-time and had no time to make an impact on the game.
Lucas Biglia: NA
Came on in the second half of extra-time and had no time to make an impact on the game.
Switzerland
Diego Benaglio: 9/10
Was Switzerland’s man of the match and almost helped his side keep a clean sheet. Made several crucial saves that kept his side in the game and could do nothing about the winning goal scored by Di Maria.
Stephan Lichtsteiner: 6.5/10
Had a largely solid game until late into extra-time when he gave the ball away near the half way line and was duly punished as Argentina took full advantage of a tired Switzerland side.
Fabian Schär: 7/10
The 22-year-old centre back who slotted in for the injured von Bergen had a solid game in the centre of defence. He made a few key interceptions and clearances and emerged out of defence with elegance and poise.
Johan Djourou: 8.5/10
Not only did he make several crucial interceptions in defence, but Djourou was calmness personified at the back, when he came out with the ball. His positioning and awareness was key to his side keeping Argentina at bay.
Ricardo Rodriguez: 9/10
Was arguably Switzerland’s best out-field player on the pitch. Not only did he do a brilliant job of marking Angel di Maria and keeping him quiet, but the Swiss full back also ventured forward with confidence.
Gokhan Inler: 7/10
The Swiss captain had a mixed game. Although he snuffed out most of the Argentine attacks and emerged out with the ball, his distribution was found wanting at times and gave the ball away quite often and was lucky that he wasn’t punished.
Valon Behrami: 7.5/10
Had a brilliant game in the centre of the pitch. Not only did he break up play well, but also came forward with the ball and his decision-making was top-notch throughout the game.
Xherdan Shaqiri: 8/10
Was Switzerland’s brightest attacking prospect. Created a couple of decent chances for his team-mates which weren’t taken and he almost won them the game with a late free kick, but it wasn’t to be.
Granit Xhaka: 5.5/10
Was arguably the least effective of all Swiss players. Not only was Xhaka ineffective going forward, but also committed some silly fouls and ran the risk of being sent off. His ineffectiveness meant that he was taken off after the hour mark.
Admir Mehmedi; 7.5/10
Displayed some brilliant ball control throughout the game and was a constant thorn in Argentina’s side. Had plenty of amazing dribbles, but couldn’t cap them off with a decent delivery.
Josip Drmic: 4/10 – Flop of the match
Although he was isolated up front for most of the game, Drmic had a couple of good chances, both of which he wasted. Early in the first half, the striker was sent through on goal with only the goal keeper to beat but he only succeeded in hitting it straight at Romero.
Substitutes:
Gelson Fernandes: 6/10
After being booked barely minutes after coming on in the second half, Fernandes had an unspectacular but solid game.
Haris Seferovic: 5.5/10
Came on for the ineffective Drmic, but he too was unable to do much in an attacking sense.
Blerim Dzemaili: 6.5/10
Although he came on only towards the end of the first half of extra-time, he almost scored the equaliser as his header hit the post and the rebound hit his leg and went out.