Uruguay had taken an early lead through Diego Perez before the midfielder was sent off seven minutes before halftime.
Argentina equalised through Gonzalo Higuain and saw Javier Mascherano red carded shortly before the end of the 90 minutes. The match produced no more goals in extra time and finished 1-1.
Uruguay will now meet Peru in the semifinals after they beat Colombia 2-0 in Saturday’s other quarterfinal.
“Today we had to fight more than play... These are two teams that came here to be champions, but this was only a quarterfinal and there’s still along way to go,” Uruguay’s captain Diego Lugano told reporters.
Argentina coach Sergio Batista told the post-match news conference he was disappointed but thought the players had given their all.
“I can’t be content because no-one likes to be eliminated but I’m satisfied with the players,” he added.
Uruguay shocked the home side by taking the lead in the sixth minute from a set-piece.
A free kick by Diego Forlan, winning a record 80th Uruguay cap, was headed back across goal by defender Martin Caceres and Perez slid in to score.
The lead did not last long as Argentina equalised 11 minutes later when Lionel Messi sent in a curling cross towards the far post where Higuain ghosted in behind the defence to score with a downward header.
Uruguay were reduced to 10 men in the 38th minute when Perez, who had been booked for going in on Mascherano with his studs showing, was shown another yellow card for obstruction.
Despite being a man down, Uruguay looked just as dangerous as Argentina with Forlan’s free kicks always a menace, although the hosts did more of the attacking with Messi delivering plenty of trademark passes into space for the forwards.
Argentina created a brilliant chance in the 79th minute when Messi chipped over the defence to Higuain, who swivelled on the spot and his rising shot was turned over for a corner by Muslera.
At the other end, Luis Suarez put Forlan through into the box but keeper Sergio Romero was quick to block. As the 90 minutes ran down, Mascherano fouled Suarez and was booked for the second time and sent off.
Muslera made another crucial intervention in the final minute, first saving substitute Tevez’s free kick then blocking Higuain’s close-range effort from the rebound. In added time, Suarez turned a defender twice on the right but his cross was just too high and Forlan headed over.
Higuain hit the near post with a shot from a tight angle with Muslera beaten just before the end of the first half of extra time and Forlan went just wide with an effort right after the team changed ends.
Peru stunner
In Cordoba, the Colombians should have taken the lead with a penalty in the 66th minute but striker Radamel Falcao put the ball wide. With game 0-0 at the end of 90 minutes, Colombia goalkeeper Luis Martinez spilled the ball when he came out at a Vargas free kick and substitute Lobaton fired into the roof of the net to put Peru ahead in the 12th minute of extra time.
Ten minutes later, with Colombia pressing for an equaliser, striker Paolo Guerrero took possession in a counter-attack and passed to man-of-the-match Vargas, who rifled home.
The first real chance came after half an hour when Falcao shot just over from winger Dayro Moreno’s pass after a rare error from central defender Alberto Rodriguez. Then Peru’s right winger William Chiroque began causing big problems for the Colombia defence. In the 34th minute, he crossed low to Vargas and the Peru captain’s shot from 20 metres forced Martinez to dive and push the ball wide.
Peru keeper Raul Fernandez then dived at Falcao’s feet to make the save while at the other end Colombia captain Mario Yepes’ diving header cleared a dangerous cross from Guerrero. A shot from Chiroque went close and Colombia scrambled away a couple more Peruvian half-chances early in the second half before creating some scoring chances themselves.
Yepes found Moreno with a good ball out of defence but the winger shot wide before Rodriguez fouled Moreno in the box but Falcao struck his penalty wide. Two minutes later, another break by Colombia ended with Moreno hitting the bar with a fierce right-footed shot.
Going into the final 10 minutes, Peru midfielder Adan Balbin had a dipping shot from 25 metres tipped over by Martinez. Midfielder Fredy Guarin almost scored two minutes into added time when he jinked past two defenders on the left, cut in and shot with Fernandez tipping the ball over the bar for a corner.
