Van Persie who plays his club football for Arsenal has recently returned from an ankle injury which he suffered playing for his National team against Italy in November.
The forward netted the two goals on the end of assists by Real Madrid's Rafael Van der Vaart and Ibrahim Afellay.
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Manchester United-bound forward Javier Hernandez pulled back a goal after the break, but a resurgent Mexico could not force an equalizer.
"We were quite impressive for the majority of the first half and we have shown what we're capable of. I've seen some very good attacks before the break," said Van Persie told Dutch television.
In the morning's other friendly, France claimed a 2-1 home victory over Costa Rica at the Stade Felix Bollaert in Lens in their farewell match before the World Cup.
Costa Rica opened the scoring on 12 minutes when Carlos Hernandez gave the Tico's a perfect start to the game with a shot from outside the box that somehow deceived Steve Mandanda.
Les Bleus were soon on even terms with Costa Rica's Douglas Sequeira turning a cross from Franck Ribery into his own goal.
France gained momentum from the stroke of luck and continued to press throughout the match until 'Le Petit vélo' Marseilles Mathieu Valbuena scored the winner in the 83rd minute skidding his shot in from 25 yards out.
France will play Uruguay, Mexico and hosts South Africa in pool A and will be hoping to go one better than their efforts in Germany 2006 when they lost the final to Italy.
