Oscar Tabarez’s side progress through to the semi-finals against Peru after dumping out the pre-tournament favourites
The match which ended 1-1 at the end of extra-time was then won 5-4 on penalties by Uruguay, who progress through to the semi-final where they will face Peru.
Uruguay, who are searching for their 15th Copa America title, took an early lead in the fifth minute as Diego Perez capitalised on a loose ball in the box.
Sergio Batista's side quickly drew level, however, as Gonzalo Higuain netted an equaliser 12 minutes later.
Uruguay's chances of grabbing a second were hindered by the sending off of Perez, who picked up a second booking for a foul on midfielder Fernando Gago.
The teams were evened up with 30 minutes to play as Javier Mascherano received his marching orders for picking up his second yellow following his foul on Liverpool forward Luis Suarez.
Fernando Muslera, who displayed a string of fine saves in normal time, prolonged his performance into the shootout as he kept out Tevez's effort from the spot.
Lionel Messi, Nicolas Burdisso, Javier Pastore and Higuain all converted their efforts for Argentina but Uruguay's strike force kept their composure as Diego Forlan, Suarez, Andres Scotti, Walter Gargano and Martin Caceres all netted from 12 yards.