The Dutchmen sent their strongly favoured opponents packing after unleashing a scintillating second half sucker-punch that saw Brazil crumble having produced a dazzling display of football in a match they had looked set to win.
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Midfielder Wesley Sneijder was the man of the moment for Netherlands, heading home the winner on 68 minutes and driving a goal-bound cross eight minutes after the break that was steered into his own net by Felipe Melo.
"It's fantastic, we are in the last four in the World Cup - we beat Brazil," an ecstatic Sneijder said.
"You have to be happy with that. If you eliminate Brazil, one of the biggest, best teams of this championship, the feeling is relief."
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Netherlands will meet the winner of either Ghana or Uruguay, who play in Johannesburg later on Friday, in their first semi-finals appearance since the 1998 World Cup.
Brazil at times played smooth, breathtaking football, with Robinho and Kaka creating chances from nothing with silky footwork and neat breaks that had the Dutch running around in circles and staring at defeat.
Robinho had an early goal disallowed for offside but got Brazil off the mark on 10 minutes when he latched on to a pinpoint 30-metre through ball from Felipe Melo to beat the onrushing keeper from inside the area.
BRAZIL SUBSIDE
Netherlands opted for tough and untimely tackles to try to disrupt Brazil's rhythm and nearly conceded a second on the half hour mark when Kaka unleashed a sumptuous strike that was acrobatically turned away by Maarten Stelkelenburg.
But the Brazilian onslaught subsided after the break when the Dutch emerged like a completely different team, with Arjen Robben in the thick of all the action, linking up well with Sneijder, and Dirk Kuyt always troubling the defence.
Netherlands levelled on 53 minutes after a rare mistake from Brazil's usually impenetrable defence. Sneijder drove in a weighted cross which keeper Julio Cesar missed completely before it hit the head of Felipe Melo and ended up in the net.
The goal was a killer blow for Brazil, who were wound up by their opponents' physical approach and fell to pieces before Sneijder popped up to head home after Kuyt flicked on Robben's 68th-minute corner.
Tempers flared throughout the match and Felipe Melo was given his marching orders 17 minutes from time after stamping on Robben, venting his frustrations at the Dutch striker's ease in tumbling to the ground under challenges.
Dutch coach Bert van Marwijk praised his players' resolve and reiterated his belief that his team were genuine candidates to lift the World Cup.
"Two years ago I said we have a
