Uruguay had taken an early lead through Diego Perez before the midfielder was sent off seven minutes before half-time.
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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 semi-finals after they beat Colombia 2-0 in Saturday's other quarter-final.
"Today we had to fight more than play... these are two teams that came here to be champions, but this was only a quarter-final 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.
MUSLERA SAVES
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,
