|Sneijder's goal meant the Netherlands were the first team into the semi-finals [GALLO/GETTY]
Wesley Sneijder scored the winner after forcing a Brazil own goal as the Netherlands put the favourites out of the World Cup with a 2-1 win in Port Elizabeth.
Sneijder headed home from Dirk Kuyt's touch as the Dutch weathered an early Brazil storm that saw Robinho stroke Felipe Melo's perfect through-ball past Maarten Stekelenburg.
But Melo headed past his own keeper Julio Cesar from Sneijder's long diagonal cross and then was sent off for a stamp on Arjen Robben as the five-time winners went out in the quarter-finals for the second World Cup running.
"In the changing-room at half-time, everyone said to each other 'let's give everything' and that's what we did. We fought for each other," Sneijder told a television reporter after the match.
"In the second half, we put a lot of pressure on their defence and to score twice was fantastic.
"We're in the last four of the world. To beat Brazil 2-1 in the quarter-final, you have to be pleased with that. But in the next days, we will have to get our heads in focus again."
Brazil took a 10th minute lead through Robinho and dominated the first-half against a Dutch team which initially looked outclassed.
But the Dutch levelled out of the blue in the 53rd minute after a rare mistake from Brazil's usually impenetrable defence, as Melo headed Sneijder's cross into his own goal.
Then Sneijder headed a winner as the Dutch, battling to their 13th successive World Cup win to maintain a perfect record in the qualifiers and finals, avenged a quarter-final defeat in 1994 and a semi-final defeat four years later.
Dutch coach Bert van Marwijk said the comeback showed how mentally strong his team were.
"In the first 20 minutes, I was happy that the score was only 1-0, and I told Frank (assistant Frank de Boer) that we still have a chance. In the second half we showed how good we are," he said.
"Tonight we're going to party and then start and fight again."
Brazil had started brightly with Melo, returning from an ankle injury which kept him out of the second round match against Chile, setting up the first goal at the Nelson Mandela Bay Stadium.
He threaded a 30-metre pass through the Dutch midfield and Robinho timed his run perfectly to score with a first-time shot.
The game turned niggly, although Brazil managed to produce some flowing moves and should have extended their lead.
Juan volleyed over from close range after a jinking run on the right by Dani Alves and Stekelenburg produced a superb one-handed save to tip away Kaka's curling effort, following a dazzling Robinho run down the left.
Just before half time, Maicon fired into the side-netting after Luis Fabiano rolled the ball into his path.
The Dutch rarely threatened with Arjen Robben far too predictable to outfox the Brazil rearguard.
But they levelled out of the blue eight minutes after the break when Felipe Melo touched Sneijder's looping cross-shot into his own net.
Kaka missed an excellent chance to put Brazil back ahead, side-footing wide from the edge of the area after the ball was gifted to him by a poor clearance.
They paid dearly in the 68th minute when Dirk Kuyt flicked on Arjen Robben's corner at the near post and Sneijder headed into the net.
Shortly afterwards, Melo was sent off for stamping on Robben, and the Netherlands wasted some simple chances to test Cesar in the final 10 minutes but held on to spark joy in Port Elizabeth and back home.