Sevilla striker Luis Fabiano bagged a brace and Liverpool defender Andrea Dossena scored an own goal as Dunga´s flamboyant troops stunned their arch rivals with the triple blow just before the break.
It was the first time Italy has conceded three goals before half-time since 1957.
With the United States recording a shock 3-0 win over Egypt in Rustenberg, Italy missed out on goal difference with Bob Bradley´s men instead unexpectedly going through to the semi-finals with Brazil.
By topping Group B, Brazil avoid Spain and play South Africa on Thursday for a place in the final after the hosts finished runner-up in Group A.
The United States take on the European champions on Wednesday.
"We showed today that we were superior in all aspects of the game. We beat the world champions and we did it in an an efficient way," said Dunga.
"We tried to have a balanced approach, keep possession of the ball as much as possible. I told the players they have to concentrate and score goals because that is what throws the other team out of kilter."
It was a lackluster display by an aging Italian team that has failed to shine with coach Marcello Lippi sure to face stinging criticism back home where he has been slammed for failing to make better use of his younger players.
"Frankly I didn´t think our condition was brilliant when we first showed up. I hoped the physical ability of the players would grow but we are going home," he said.
"We are disappointed with our performance and we are very much aware of that. This does not reflect the way we usually perform. We were certainly not at our best in this championship."
An apathetic Italy slumped to a shock 1-0 defeat against Egypt in their last group game and Lippi made four changes to try and reverse the slide.
Out went Fabio Grosso, Gennaro Gattuso, Giuseppe Rossi and Fabio Quagliarella and in came Andrea Dossena, Riccardo Montolivo, Luca Toni and Mauro Camoranesi.
But it made little difference against a Brazilian team that took full advantage of Italy´s defensive frailties.
They were dangerous from the outset with Italy fortunate not to go behind after six minutes when Ramires hit the angle between the post and the crossbar after being put through by Fabiano.
Italy were forced to get men behind the ball as the South Americans surged forward, Maicon and Kaka both having shots blocked and Robinho forcing a save from Gianluigi Buffon.
They eventually settled down but the Brazilian pressure was relentless and Daniele de Rossi almost put the ball in his own goal when he stuck out a foot to meet a Lucio shot and it deflected onto the post.
The breakthrough came eight minutes before half-time when Fabiano pounced on a scuffed shot from Maicon to drive the ball beyond Buffon´s reach.
They doubled their lead six minutes later when Robinho and Kaka combined to feed Fabiano who made no mistake from close range.
With Italy on the ropes, Brazil delivered a knockout punch two minutes later after Robinho broke down the left and delivered a cross with Dossena turning the ball into his own net under pressure.
Italy finally woke up in the second half with substitutes Simone Pepe, Giuseppe Rossi and Alberto Gilardino all getting shots on target as they desperately tried to restore some pride.
Their best chance came when Pepe had a shot blocked with goalkeeper Julio Cesar stranded, but despite last ditch efforts they failed to redeem themselves.
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