Julian Alvarez and Lautaro Martinez scored in extra time to send Argentina through to a World Cup semi-final showdown with England, but their win over Switzerland again found them at the centre of controversy after a series of key decisions went in favour of the world champions.
Argentina led through Alexis Mac Allister's first-half header, but Switzerland grabbed a deserved equaliser on 67 minutes courtesy of Dan Ndoye.
Minutes later, a piece of World Cup history was created as Leandro Paredes was the beneficiary of mistaken identity.
A VAR review showed the Argentina midfielder was innocent of tripping Breel Embolo. Paredes had his yellow card rescinded by referee Joao Pinheiro, and, having already been booked, Embolo was cautioned a second time for simulation and sent off.
Argentina entered the game under a cloud after the Egyptian Football Association accused match officials and Fifa of bias towards the world champions following Tuesday's 3-2 defeat in the last 16.
Switzerland will have similar sentiments. The 50-50 calls seemed to favour Argentina, although Embolo's second yellow card did appear to be the correct decision.
With penalties looking inevitable, Alvarez scored with a world-class strike, and with Switzerland pushing players forward for an equaliser, Martinez was on hand to slot home a rebound for Argentina to prevail 3-1 and keep their World Cup title defence on track.
Argentina were unchanged from their last-16 win over Egypt, with coach Lionel Scaloni keeping faith with Nicolas Tagliafico at left-back and Leandro Paredes in midfield.
When Lionel Messi last played in Kansas City, he lit up the tournament with a mesmerising hat-trick in a 3-0 win over Algeria in the group stage.
He was much more subdued against Switzerland, although he did provide the corner for Argentina's first goal.

The Swiss last lost a competitive match in November 2024. Indeed, Murat Yakin’s side were the only team left in the tournament yet to trail in any match. That record fell in the 10th minute, with Mac Allister heading in a Messi corner.
Djibril Sow tested Emi Martinez’s concentration with a long-range drive, and the Argentina goalkeeper was equal to it.
Martinez was again alert as Embolo bore down on goal on 31 minutes. The Aston Villa goalkeeper raced off his line and showed bravery in diving at the Swiss striker’s feet.
Granit Xhaka was seeing plenty of the ball, but the Swiss captain’s sense of frustration was evident when he picked up a yellow card for a crunching tackle on Rodrigo De Paul.
Embolo was next to have his name taken by the referee after being penalised for a clumsy challenge on Paredes as the half drew to a close.
Other close calls seemed to fall Argentina's way. Switzerland's frustration was palpable.
They should have equalised on 49 minutes. Lisandro Martinez was caught napping, failing to track Embolo’s run. He squared the ball for Ndoye, but Martinez atoned with an important block that deflected Ndoye’s effort out for a corner.
Martinez was again at his best to deny a Ndoye header. Xhaka was next to test the Argentine goalkeeper with a fizzing left-foot strike but Switzerland could find no way past.
Switzerland were dominating possession and there was a growing sense that they would soon get the breakthrough.
It came in the 67th minute, and it was no surprise that Ndoye got it.

The Nottingham Forest winger had been Switzerland’s biggest attacking threat. After collecting the ball wide on the left, he played a neat one-two before drilling a shot that clipped Martinez’s outstretched leg on its way to goal. It was no more than Yakin’s side deserved.
Then came Embolo’s moment of madness. Paredes was initially booked for a foul, but after a VAR review for mistaken identity, the referee rescinded Paredes’ yellow and issued Embolo a second yellow for simulation instead.
Having already been booked, Embolo was given his marching orders. He was inconsolable. There was a case to be made that he simply tripped himself up, but replays confirmed that VAR made the right call.

Argentina had a one-man advantage and that seemed to briefly spark Messi into life.
Positioned mostly on the right, the maestro failed to have the sort of impact that has seen him guide Argentina comfortably through the group stage and in testing knockout matches against Cape Verde and Egypt.
The last time Argentina’s captain failed to score in a World Cup match was against Poland in the group phase at the 2022 tournament – 10 matches ago.
He had a chance to add to his eight goals at this tournament on 84 minutes, but failed to get enough elevation on his shot to clear Gregor Kobel, who was saved by the offside flag in any case.
Nine minutes of added time were signalled. Messi caught everyone by surprise when he switched the ball to his right foot, but his whipped effort went agonisingly wide of Kobel's post.
Having been mostly static, Messi was now energetic. Crosses were sent in for teammates. Give-and-goes were played on the edge of the box. A Martinez volley from a Messi corner was parried by Kobel.
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In extra time, Thiago Almada had Swiss hearts in their mouths, but his shot rippled the outside netting.
Switzerland were reduced to long-range efforts as they parked all nine outfield players behind the ball.
Messi tested Kobel again, but Alvarez finally found the breakthrough with a moment of magic.
Collecting the ball just outside the area, he let rip with a world-class strike that nestled in the top corner. Substitute Martinez added a third at the death following a swift counter-attack to finally put the game to bed.
The scoreline flattered Argentina, and it was the third knockout round in a row they needed extra time to progress.
England are up next in Atlanta on Wednesday. Beat them and Messi will appear in his third World Cup final, equaling the record of Brazil defender Cafu.
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