Carlos Tevez, on as a late substitute, missed the crucial spot-kick at the Santa Fe Stadium, as the hosts crashed out to extend a trophy drought going back to 1993.
Diego Perez had given Uruguay a fifth-minute lead but Gonzalo Higuain levelled 12 minutes later. Both sides ended the 90 minutes with ten men. Perez was sent off on 38 minutes for a second yellow card and then Argentina lost captain Javier Mascherano in the 86th minute for a bad tackle from behind on Luis Suarez.
The extra half-hour failed to end the stalemate and Martin Caceres drove home the winning penalty as Uruguay moved into a semi-final against Peru, 2-0 conquerors of Colombia.
"This was like a final. We played an Argentine side with a fantastic attack and had to scrap - but we have put out our biggest rivals," said Uruguay defender Diego Lugano.
Uruguay, who have won a joint-record 14 Copa titles along with their hosts from across the River Plate, wasted no time in breaking the deadlock just seven minutes into the contest.
Perez puts Uruguay ahead, receives red
Perez slid the ball home from close range, following up after home shot-stopper Sergio Romero could only palm away a header from Caceres, who had nodded down a Diego Forlan cross.
But Argentina hit back and Lionel Messi inspired the equaliser, conjuring an exquisite cross from the right which hung in the air the fraction of a second required for Higuain to leap and meet the ball full on, dispatching it past Fernando Muslera in the 17th minute.
Messi punched the air as he yet again provided the creative spark which had been in such short supply in drawn group games with Bolivia then Colombia.
On the half-hour, the recipe was centimetres away from working again - Higuain heading in a Messi free-kick only to be judged fractionally offside. Caceres then drove home for the Uruguayans but also saw his effort ruled out for offside.
That was bad enough for Uruguay, but then seven minutes before the interval they were reduced to ten men after Perez barged into Messi and was dismissed by Paraguayan referee Carlos Amarilla - whose name ironically means yellow. As well as brandishing the pair of reds, Amarilla also booked nine players - six for fired-up Argentina.
Messi, desperate to end an 18-year trophy drought for the Argentinians and prove he can be a world-beater at international as well as club level, then fired a low left-foot shot that Muslera gathered easily in the Uruguayan goal.
The Barcelona man tried again, feeding Angel Di Maria down the inside left channel, but he could only shoot into Muslera's midriff. Messi then found Higuain, but his shot on the turn drew a smart stop from Muslera.
Mascherano given marching orders
With four minutes to go to the end of normal time, Argentina had skipper Mascherano sent off for a clumsy rather than crude challenge from behind on Liverpool man Suarez. Having to find fresh impetus, Argentina coach Sergio Batista threw on Tevez for the final half-hour's denouement
Tevez promptly drove over, before Javier Pastore did likewise, his shot clearing the bar by just centimetres. At the other end, Forlan, still without a goal for the Celeste since last summer's exploits in helping his countrymen to the FIFA World Cup™ semi-finals, floated a left-footer off target as penalties loomed.
Desperate to avoid that lottery, Messi escaped a clutch of defenders but Muslera covered his low shot. Tevez then combined with Messi - the pairing's compatability, or lack of it, being one of the tournament's most discussed topics - but the Barcelona man was crowded out and the shootout became unavoidable.