The result maintained Brazil's proud record of never having missed a FIFA World Cup. It also piled more pressure onto Argentina coach Diego Maradona whose team are clinging onto the fourth and final automatic qualifying spot from the South American zone.
In a first-half played at a breathless pace, the tackles came thundering in and it was hardly surprising that Brazil's two opening goals were the product of set pieces. Benfica skipper Luisao scored the first from an Elano free-kick in the 24th minute when the defender was allowed a free header, which he buried in the corner past Mariano Andujar in the Argentine goal.
It was 2-0 just six minutes later after Kaka was brought down on the edge of the box. This time Elano's free-kick was blocked by a defender but Kaka managed to set-up Gilberto Silva whose fierce drive was only parried by Andujar. Sevilla striker Luis Fabiano pounced on the loose ball to score from six yards out.
Argentina had their moments with Lionel Messi and Carlos Tevez always looking dangerous. It was Tevez who cleverly set-up Maxi Rodriguez for the home side's best chance in the first half but Julio Cesar saved with his legs from point-blank range.
Argentina pulled a goal back in the 65th minute thanks to a 30-yard left foot drive from Jesus Datolo which soared past Julio Cesar into the top corner. However, Brazil were 3-1 ahead within two minutes when Kaka played a wonderfully-weighted pass into the path of Fabiano who sprinted around Nicolas Otamendi before chipping the ball over Andujar for his second goal of the tie.
Earlier, Brazil's chances of wrapping up qualification had been boosted when Colombia defeated Ecuador 2-0 in Bogota while Uruguay slumped to a 1-0 loss in Lima to bottom side Peru. Jackson Martinez and Teofilo Gutierrez scored for Colombia in the last ten minutes while Hernan Rengifo claimed Peru's winner four minutes from time to register just his team's second win in 15 qualifiers.
Colombia, who moved into fifth place in the table, just outside the four automatic qualifying places, had their celebrations cut short when central defender Fabian Vargas picked up a serious leg injury which will rule him out of Wednesday's game with Uruguay.
Paraguay, meanwhile, boosted their hopes of qualifying with a 1-0 win over Bolivia. Salvador Cabanas, with a penalty on the stroke of half-time, gave Paraguay the three points which also ended Bolivia's slim hopes of qualifying for the finals.