A superb goal eight minutes into extra-time by Maxi Rodriguez sealed Argentina's 2-1 win over Mexico here on Saturday and a mouth-watering clash with Germany in the World Cup quarter-finals next Friday.
Regulation time had finished 1-1 after two goals in an action-packed first quarter, but it was a moment's brilliance from Rodriguez that ensured Mexico would not make their third ever World Cup quarter-final.
The Atletico Madrid midfielder chested down an innocuous Juan Sorin pass on the edge of the area, swivelled and fired a looping left-footed volley into the far top corner beyond the reach of diving goalkeeper Osvaldo Sanchez.
"That was incredible," said Rodriguez. "It was a really tough game, with Mexico making it very difficult for us but we came through in the end," said Rodriguez, who raced ecstatically to his bench to be engulfed.
"Now we are confident we can go further and beat anyone."
To do so they will now have to knock out the hosts.
Argentine coach Jose Pekerman said Argentina had taken their chance when it belatedly came.
"It's vital to take the chance when it arrives in as well-balanced a meeting as that between two rivals who know each other so well. And we did - deservedly so," Pekerman said
Mexico put the early pressure on and the strategy paid off in the sixth minute.
Captain Rafael Marquez lost Gabriel Heinze to come rushing in to the far post unopposed to drive home a Pavel Pardo free-kick which Mario Mendez headed on.
Argentina responded immediately, pressure from Hernan Crespo forcing Jared Borgetti, who was returning after missing the last two games through injury, to head Juan Riquelme's swirling corner into his own net in the 10th minute.
Lacking the incisive passing and running of Lionel Messi and Carlos Tevez, both benched by coach Jose Pekerman despite their outstanding display in the goalless draw against the Netherlands, Argentina looked one-dimensional against a dynamic Mexico.
Borgetti, who scored 14 goals in Mexico's qualifying run, was a constant threat to Argentina, whose strikers were continually thwarted by the stout defending of the outstanding Marquez, Carlos Salcido, Ricardio Osario and Andres Guardado.
Last-ditch defence by West Ham defender Lionel Scaloni deflected Borgetti's header in the opening minutes, Heinze was forced into a sliding block on a vicious shot after 14 minutes, and goalkeeper Roberto Abbondanzieri then tipped a blistering 25-yard shot over the bar.
Crespo was almost on the scoresheet five minutes later, the Chelsea striker's lob off a delicate Cambiasso chip beating goalkeeper Oswaldo Sanchez but also the far post.
The first-half ended in controversy when Heinze, who put in for him a rare sloppy performance in the first-half, miscontrolled a simple pass from Abbondanzieri and gifted the ball to Francisco Fonseca before hacking down the striker.
Swiss referee Massimo Busacca doled out a yellow card for the Manchester United defender but it could easily been red.
Marquez alluded to that afterwards in saying that "various refereeing decisions went against us - but in the end the team that scores more goals wins. We gave our all and it's sad."
Fonseca had a clear chance in the 54th minute, failing to control a ball with just the Argentine keeper in front of him.
Straight up the other end, Sanchez beat away a shot from Rodriguez, largely outmuscled until then.
And Sanchez made the save of the match a minute later, showing great reflexes to parry a well-driven Javier Saviola shot around the post.