Having matched their rivals for a good part of the clash in Mendoza, goals from the Barcelona and Manchester City men sank the Celeste in the second half to keep the hosts top
Sergio Aguero was the other man to get on the scoresheet in a brilliant second-half flurry, which puts the Albiceleste back at the top of Conmebol's World Cup qualifying competition at the halfway stage.
Argentina enjoyed a lion's share of possession during an entertaining first half in Mendoza, but struggled to break down a Uruguay unit who did not shy away from taking on their eternal rivals.
It took a moment of magic from Lionel Messi to open up the defence for the first time; the Barcelona phenomenon drew in the defence with a mazy run before opening the game for Angel Di Maria, whose effort was stopped by Fernando Muslera in the Charrua net.
Clean chances were at a premium throughout the opening 45 minutes. The home team passed well and tried valiantly to make space, but too often fell at the final hurdle. Messi was again at the centre of the action when an outrageous individual dribble left two markers prostrate. 'La Pulga', however, was denied a stunning goal when his looping shot struck the top of the woodwork. Muslera then intervened once more to stop Lio making the difference, acrobatically punching a free-kick over his own crossbar.
Uruguay were not sitting back despite seeing little of the ball, and towards the end of the half created their first decent opportunity. An intelligent header from Martin Caceres found Luis Suarez with space, but the striker's half-volley was safely grabbed by Sergio Romero.
Edinson Cavani also had one of the visitors' few openings from distance, but Oscar Tabarez's men would have been content enough to go into the break level after sustaining heavy pressure. Argentina were on top, but needed more precision in front of goal if they were to take three points and return to the top of the Conmebol standings at the final whistle.
Just two minutes into the second period, Ezequiel Garay had a golden chance to put his team ahead. A looping free kick from Messi caught out the Uruguay defence, but the centre-back could only scoop his first-time effort over when the goal was gaping.
The Celeste were then somewhat lucky to keep all 11 men on the pitch; Diego Lugano invoked the home fans' fury with a vicious tackle on Romero, but was only shown the yellow.
The game was quickly taking on a nasty appearance, with tackles flying in indiscriminately particularly from the visitors. But in spite of the disruption, Argentina continued to seek their first of the evening. The Estadio Malvinas Argentinas held its breath when Gonzalo Higuain received Aguero's cross free at the far post, but a feeble left-footed effort dribbled wide of the post to the relief of Uruguay. 'El Kun' next opted to go alone from 20 yards out, his shot flying straight into Muslera's arms.
With 20 minutes gone in the second half, the breakthrough finally arrived to the joy of the home fans. Patient build-up from Argentina left Di Maria with space on the edge of the area, but the Real Madrid star spurned the chance to shoot in favour of an intelligent passed poked home by captain Messi. Coach Alejandro Sabella leaped off the bench in delight, as the Ballon d'Or holder celebrated his 29th goal in international colours.
The game was decided shortly after with a team goal of clinical beauty. Aguero, Messi and Di Maria ripped the Uruguay defence to pieces on the break after a sloppy loss of possession, and it was again Angel's pass that was coolly tapped home by 'El Kun' to confirm the victory for the rampant Albiceleste.
And insult was added to injury for the Celeste with 10 minutes to go, courtesy of Messi who surgically placed a free kick under the wall and into the corner of the net to seal a 3-0 trouncing.
The win puts Argentina back to the top of their World Cup qualifying group with 17 points from their first eight matches, leading Ecuador and Colombia who also recorded victories on Friday. Uruguay, meanwhile, lie in fourth place just inside the group of teams that would earn automatic passage to Brazil 2014.