With the result, the Netherlands finishes a World Cup unbeaten in regular play for the first time, having lost to Argentina on penalties in the semifinals. After finishing runner-up in 2010, the third place is the best position for the Dutch squad since it lost the final in 1974 and 1978.
The loss added to Brazil's frustration at the home tournament following the disastrous 7-1 defeat to Germany. After the final whistle, the team was loudly booed by the nearly 70,000 fans that attended the match at the National Stadium in Brasilia. Many had already left even before the late third goal by the Dutch.
''It's a terrible feeling, I don't know what to say,'' Oscar said. ''After a huge loss to Germany, today we tried our best from the beginning to win third place but it wasn't our day. We have to see what went wrong so we can improve for the future.''
Van Persie converted a penalty kick three minutes into the match after Arjen Robben was brought down by Brazil captain Thiago Silva on the edge of the area. Blind added to the lead in the 17th with a shot from near the penalty spot after defender David Luiz made a mistake while trying to clear a cross in front of the goal. Georginio Wijnaldum rounded off the win in injury time with a shot inside the near post.
''The most beautiful was our resilience. We were knocked out but we came back and finished third,'' Wijnaldum said. ''We wanted to close it out well.''
Brazil looked lost from the start, making many of the same defensive mistakes that marked the historic defeat to the Germans four days ago. The Netherlands took advantage with quick passes and speed in the attack.
Silva had to foul Robben after being beaten on the run, leading to van Persie's firm left-foot shot into the right upper corner to put the Dutch ahead.
The Dutch wanted a red card for Silva for a professional foul, but Algerian referee Djamel Haimoudi only gave him a yellow. Silva had missed the semifinal against Germany because of a yellow card suspension.
Blind added to the lead after Luiz failed to clear a cross, heading the ball right back to the Dutch defender for an easy goal.
Wijnaldum closed the scoring in injury time with a goal from inside the area after a cross by Daryl Janmaat.
''It is a good end,'' Robben said. ''You can wipe away the hangover (of the lost semifinal). I'm so proud. Compliments to this team. It's a party to work with this team. We deserved more.''
Brazil's best chance in the first half came on a free kick taken by Oscar in the 36th, but Silva and Luiz were not able to reach the low cross in front of goal. In the second, Ramires came close with a low right-foot shot from the top of the area in the 60th.
Brazil wanted a penalty when Oscar went down in the area in the 68th, but the referee instead gave a yellow card to the Brazilian for diving.
''It's frustrating,'' Silva said. ''We didn't deserve to have it end like this. But unfortunately it's football. I have to apologize to our people. The fans supported us even during the 7-1 loss and again today. They booed in the end, but it was normal. They have feelings too.''
It was the fourth time Brazil played in a third-place match. It beat Sweden in 1938 and Italy in 1978, and the only other loss had come against Poland in 1974.
The Netherlands had played in the third-place match one other time. It fell to Croatia 2-1 in 1998 after being beaten by Brazil in the semifinals.
Brazil coach Luiz Felipe Scolari made six changes from the team that started in the loss against Germany, the national team's worst defeat in its 100-year history.
Netherlands: Jasper Cillessen (Michel Vorm, 90); Dirk Kuyt, Ron Vlaar, Stefan de Vrij, Bruno Martins Indi, Jordy Clasie (Joel Veltman, 90), Daley Blind (Daryl Janmaat, 70); Georginio Wijnaldum, Jonathan de Guzman; Arjen Robben, Robin van Persie.
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