Carried on a wave of incredible support, Argentina overcame a 10-0 deficit to eventually overwhelm Wales 29-17 as late tries by replacements Joel Sclavi and Nicolas Sanchez took them into the World Cup semifinals for the third time on Saturday.
Wales made all the early running and deservedly led after a Dan Biggar try but Argentina chipped back with a series of Emiliano Boffelli penalties to take the lead.
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Wales were on the back foot for most of the second half, and though a Tomos Williams try briefly restored their lead, there was a sense of inevitability about Argentina's emphatic response amid a raucous sea of blue.
It was a remarkable turnaround for Argentina in the same ground where they were brushed aside by England in their opening pool game five weeks ago and they will play either Ireland or New Zealand, who meet in Paris later, next week.
"Wales were a really good and tough team as they always are," Argentina captain Julian Montoya said. "We knew it was going to be very tight. We like to be a team that fights for everything. [It was] far from perfect but we are going to Paris [for the semi-finals].
"It's how you embrace the moment and fight for each other. That's what rugby is about. Two more weeks with this team. I don't want this to end, ever."
It was tough for Wales, who had won all four of their group games and had high hopes of a third semi in four tournaments, but they can have no complaints as their early control completely disappeared.
"We knew they were going to be a physical team but a couple of errors let us down," Wales captain Jac Morgan said
"In all fairness, they capitalised. Devastating for the boys."
After Argentina started full of attacking intent, Wales turned things round with the opening try after 14 minutes when Biggar combined with George North and a rampaging Gareth Davies, who then sent Biggar in under the posts.
It was almost all Wales for the next 20 minutes but they added only the conversion and a Biggar penalty and the Pumas hit back at the end of the half.
A sustained five minutes of pressure brought Boffelli two penalties to make it 10-6 at the break, though Wales fans were unhappy at another controversial TMO intervention.
Original referee Jaco Peyper suffered an injury and was replaced by Karl Dickson, who rightly penalised Josh Adams for a needless check on Tomas Cubelli, but was not shown replays of a subsequent assault by an Argentine that may well have reversed it.
A Boffelli penalty closed it to within a point at the start of the second half and he then comfortably banged over another from inside his own half to put the Pumas 12-10 ahead.
The Argentine fans ramped up the volume even more, creating a magnificent atmosphere that visibly lifted their men as Wales struggled to regain any sort of foothold.
But they exploded back into the lead with their first attack of the half after 56 minutes as replacement scrumhalf Williams threw a dummy that the entire Puma defence bought, allowing him to scamper through from the back of a ruck.
It proved a rare moment of action in the Argentine half though as the Pumas dominated the next 15, threatening with a series of lineout drives culminating in the massive Sclavi forcing his way over and Boffelli converting to reclaim the lead at 19-17 with 10 minutes to go.
Wales finally got going again but a brilliant diving tackle by Matias Moroni denied Louis Rees-Zammit in the corner as the winger appeared destined to score, and it proved a crucial intervention.
As Wales pressed desperately in the final minutes, Sanchez picked off Sam Costelow for a halfway line interception and raced in under the posts. Boffelli joyously converted and Sanchez polished it off with a penalty to send the Pumas to Paris.
