The Manchester United striker slotted home the only goal of the game after just six minutes when he was left with a simple finish after being set up by Wesley Sneijder.
Holland missed a number of chances to increase their lead, most notably through Arjen Robben, but they kept Ghana out at the other end to record their first victory since defeating Turkey last October.
Since that match the Dutch have drawn with Japan, Colombia and Ecuador, while losing 2-0 to France in Paris.
For Ghana, the defeat will be a disappointment but of more concern for coach Kwesi Appiah was the serious-looking injury suffered by Jerry Akaminko, who was carried off on a stretcher late on after appearing to land awkwardly on an ankle.
With the start of the World Cup just over a fortnight away, it remains to be seen if the Eskisehirspor defender will be able to feature in Brazil.
Holland coach Louis van Gaal named a strong line-up for their penultimate friendly match before they kick-off their World Cup campaign against Spain on June 13, and three of his star names combined to open the scoring early on.
Robben sent Sneijder racing into the area and the Galatasaray playmaker cut the ball back as Ghana goalkeeper Adam Kwarasey came out to meet him, giving captain van Persie an easy tap-in into an empty net.
Robben should have made it 2-0 soon after but contrived to miss a great chance from close range, before the winger saw an effort blocked by Kwarasey.
The Bayern Munich winger was again denied by Kwarasey just before the break and, continuing the theme, the Ghana keeper parried another Robben shot midway through the second half.
In the closing stages Ghana pushed for an equaliser but the unmarked Andre Ayew headed well over when he might have been better served bringing the ball down, while the same player saw a deflected shot saved by Jasper Cillessen as the match entered stoppage time.
After Akaminko's injury, Holland had a great chance to add a second right at the end but Jeremain Lens fluffed his header from six yards out.