A Dan Biggar try and five points from his boot gave Wales a 10-6 lead going into half-time, but Emiliano Boffelli nudged the Pumas in front with his fourth penalty in the 48th minute.
Tomos Williams then darted over to hand the lead back to Wales, before Joel Sclavi dived over from close range to give Argentina a two-point lead following the conversion.
Sanchez then put the finishing touches on the victory with an intercept try that saw him flooded by his jubilant team-mates in the in-goal area, before slotting a penalty in the last act of the game to steer his side into the last four of the competition.
“It was a difficult match,” Boffelli, the Mastercard Player of the Match, said. “I am very happy for the team.
“[Head coach Michael Cheika told us at half-time] That we need to keep going and keep going and that at some time the game would open for us.”
“I am very proud of the team,” captain Julián Montoya said. “We like to be a team that fights for everything. [It was] far from perfect but we are going to Paris.
“Life is not perfect. It’s how you embrace the moment. That’s what rugby is about. Two more weeks with this team. I don’t want this to end ever. We need to be better, to be clinical in a lot of things.”
Wales captain Jac Morgan admitted it was a “devastating result” for his team: “We knew they were going to be a physical team but discipline and a couple of errors let us down. We let them into our half and they capitalised on that. We let them have more possession and they got points out of it.”
Head coach Warren Gatland was gracious in defeat: “I am not going to take anything away from Argentina. They were tough and stayed in the fight and you have got to give them credit and congratulate them. They hung in there. We probably weren’t at our best but we were up against a good side who took their chances.”
So can Argentina go all the way? “I don’t know if we’ll go with the sweeping statements just yet,” a clearly delighted Cheika said. “We will wait and see. We are just thrilled to be going to Paris, we haven’t had a taste of it yet at this World Cup.
“We will look at tonight’s game and I know we won’t be favourites [in their semi-final] but we’ll be giving it our best.”
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