Brazil immediately began to press high looking to force a mistake that would let them back into the game, but in doing so left themselves exposed at the back.
It was a tactic that when combined with yet more suicidal defending from David Luiz would lead to the Dutch doubling their advantage after 17 minutes.
A weak headed clearance from the former Chelsea defender fell at the feet of Blind who had what seemed like an age to take two touches to set himself before firing the ball beyond Cesar with his third touch.
Brazilian fans would have been forgiven for fearing the worst at this stage.
But the five times world champions composed themselves as the match progressed.
They had a penalty claim of their own turned down midway through the second half after Blind appeared to clear out Oscar in the area.
Wijnaldum's neat finish in the 90th minute, meanwhile, was one of the few clear shots on goal the Netherlands had in the second half.
Still, the gulf in class was obvious throughout and not what the world has come to expect from the land of Pele, Garrincha, Zico, Socrates, Romario and Ronaldo.
Neymar and Silva aside, Brazil have looked little more than average throughout the tournament, drawing on good fortune and favorable refereeing decisions to make it past decent but limited teams like Croatia, Mexico and Cameroon.
A physically robust approach, meanwhile, was deployed against more skilful teams like Chile and Colombia.
As a result, few sides have committed as many fouls as Brazil.
This is a particularly galling statistic for the once renowned samba kings, emphasizing the negative, spoiling nature of much of their play over the last four weeks.
Gone are the days, for now at least, of ball-playing midfielders who could flummox opponents and onlookers alike with their skill, style and mastery of the ball.
Instead, powerful players like Fernandinho, Luiz Gustavo and Paulinho graft in the midfield engine room for the vintage of 2014.
More technically adept talent like Philippe Coutinho, Lucus Moura and even Ronaldinho have been squeezed out of the team and the squad as a result.
There might be plenty of muscle in this Brazil side but at times the hosts also have seemed like a collective nervous wreck. Tears have been shed during the playing of the anthem before games and after penalty shootouts.
For the Netherlands, change is also afoot.
Van Gaal will depart to manage English Premier League team Manchester United and Guus Hiddink will arrive to plot the path to the European Championships in France 2016.
Another group of fine young Dutch players have made their tournament debuts in Brazil as the old stagers like Van Persie, Robben, Dirk Kuyt and Sneijder have possibly played their last World Cup.
The likes of Bruno Martins Indi, Memphis Depay, Jasper Cillessen, Blind and Stefan de Vrij have all equipped themselves well.