Brazil saw off the challenge of a slightly disappointing Chile to seal a mouth-watering quarter-final tie against the Netherlands.
The Selecao defeated Chile 4-2 and 3-0 in World Cup qualifying - and Dunga's team eased to a comfortable victory at Ellis Park on Monday as their opponents became the first South American team to be eliminated from the competition.
Chile, shorn of suspended trio Marco Estrada, Waldo Ponce and Gary Medel, were always up against it after conceding twice in four minutes shortly after the half-hour mark.
Juan opened the scoring with a powerful header and Luis Fabiano slotted into an empty net to finish off an attacking move of lethal precision as Brazil took another step towards a sixth World Cup title.
A precise right-foot finish from the edge of the area saw Robinho, who had a later effort ruled out for offside, open his account at the tournament in the second half.
Brazil boss Dunga has been heavily criticised back home for constructing a team that values efficiency ahead of flair, but his side controlled the vast majority of the match and were comfortable winners.
Chile, as with Mexico against Argentina on Sunday, really took the contest to their opponents in the opening minutes.
Marcela Bielsa's side have won many admirers in South Africa with their quick-fire, skilful brand of attacking football, but apart from a weak Humberto Suarez shot that Brazil keeper Julio Cesar easily collected they had little end product to show for their bright start.
Brazil, with Dani Alves superb on the right of midfield, gave Chile no room to breathe and gradually took control of the contest.
They should have been awarded a penalty when Lucio was brought down by a late tackle from Pablo Contreras, but eventually took the lead through Juan's header from Maicon's corner.
The Brazil defender was left unmarked - and his perfectly placed header clearly rattled Chile, whose increasingly erratic passing prevented them from picking any holes in their opponents' defensive structure.
The tie was as good as won when Brazil scored their second just four minutes after Juan's header, with a goal of breathtaking movement and precision.
Robinho cut inside before playing a square ball to Kaka, who delivered a beautifully weighted first-time pass that Luis Fabiano, in an onside position, collected before easing past Claudio Bravo and slotting into an empty net.
The striker almost doubled his tally with a glancing header that flew wide, but Robinho sealed victory just before the hour mark with his precise finish after the impressive Ramires finished a surging run with a accurate pass. Ramires was later booked and will miss the match against the Dutch.
Bielsa had made all three substitutions with 30 minutes remaining as he chased the game and Jorge Valdivia almost pulled a goal back with a clean strike that narrowly flew over the crossbar shortly after his introduction, while Julio Cesar denied Suazo, who later clipped the crossbar.
Brazil slowed the pace of the contest but attacked in occasional devastating bursts that saw Robinho twice come close to a second goal.
He had an angled strike saved by Bravo and later slotted beyond the Chilean keeper, but was denied by a marginal but correct offside decision.
It made no difference to the outcome of a tie already over, but the five-time world champions will face a stiffer test against the Dutch in Port Elizabeth on 2 July.
Attempts on target
Attempts off target
Projected table based on current scores
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