Uruguay then lifted the Fraternity Trophy that had been put in play by winning a shootout 4-3 after Robin van Persie had blasted the opening penalty over the bar.
Luis Suarez, Kuyt's Liverpool team-mate, put Uruguay ahead eight minutes from time.
Edinson Cavani pulled the ball back from deep on the left into the middle where Suarez calmly picked his spot to place the ball inside goalkeeper Tim Krul's left-hand post.
When a Uruguay win looked certain, Kuyt glanced a corner to the near post over midfielder Sebastian Eguren and goalkeeper Fernando Muslera into the net.
"I think it was a fair result," Uruguay coach Oscar Tabarez, preparing his side for next month's Copa America in Argentina, told reporters.
In the shootout Krul, who kept a clean sheet on his debut in a 0-0 draw with Brazil in Goiania on Saturday, saved from Ajax Amsterdam's Nicolas Lodeiro but Eljero Elia then missed for the Dutch.
Both sides, meeting for the first time since the Dutch won their 2010 World Cup semi-final 3-2 in Cape Town, had chances with Suarez being denied a first-half goal for offside.
Muslera saved well with his foot from Klaas-Jan Huntelaar who was through on goal and Uruguay captain Diego Lugano was lucky to not even be booked for a studs-first foul on Van Persie.
