The Manchester United star, 30, scored twice as Holland humiliated the reigning world and European champions in the Group B opener in Salvador on Friday.
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He equalised for the Dutch with a superb diving header just 90 seconds before the break after Spain’s Xabi Alonso had converted a first-half penalty.
Van Persie then added his second and Holland's fourth when he beat Spain goalkeeper Iker Casillas to a loose ball and tapped the ball into an empty net with 72 minutes gone.
The Dutch ran riot in the second-half claiming four goals without reply as Arjen Robben also netted twice, while defender Stefan de Vrij headed home to make amends for conceding the converted Alonso penalty after fouling Diego Costa.
Holland now faces Australia next Wednesday in Porto Alegre, but Van Persie says they must build on their win and forget any dreams of reaching a second consecutive World Cup final.
“We’ve beaten the best team in the world for the last six years, and if you look at how much we wanted it and how well we played, it’s a massive compliment to the team,” the Dutch man-of-the-match said.
“We have to take it all in and enjoy it, but then focus on Australia. This was an incredible evening for the whole of Holland, but it’s only three points.”
Van Persie has a history of being part of Dutch squads who dazzle in the group stages at major tournaments, only to bow out in the knock-out stages.
Having made his international debut in 2005, Van Persie was part of Marco van Basten’s Dutch squad that was beaten by Portugal in the last 16 of the 2006 World Cup.
He was also in the squad when the Netherlands humbled both Italy and France at Euro 2008 to dominate their group, only to bow out in the quarter-finals 3-1 against Russia.
The Dutch avenged their 2010 World Cup final defeat to Spain in emphatic style, but memories of the Euro 2012 group stage exit are still fresh having lost all three games to Germany, Portugal and Denmark.
Van Persie said the squad needs to work together to improve if they are to become the first European side to win the World Cup in South America.
The Dutch were the last team to reach a World Cup final in South America, having lost to Argentina 3-1 after extra time in 1978.
“I’ve been here before, this is my fifth tournament and I don’t want us to be too excited, because this is just one game and three points,” he said.
“We have to improve and we have to stick together.”
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