**An own goal by Daniel Agger and a late Dirk Kuyt effort helped Holland begin their World Cup campaign with a comfortable victory over Denmark at Soccer City.
Both goals came in the second half after an assured first period of defending by the Scandinavians, who constantly thwarted a Dutch attack which appeared short of ideas without the injured Arjen Robben.
Van Persie and Rafael van der Vaart then played a neat one-two, but the latter saw his shot deflected wide by Agger.
The Danes had their best opening of the half just after the midway point when Bendtner found himself in space inside the six-yard box, but he could only head Dennis Rommedahl's cross from wide on the right.
The Ajax goalkeeper was drawn into his first testing save after 36 minutes when Bendtner released Thomas Kahlenberg, whose shot was acrobatically palmed away.
Just before the break, Van Persie seemed unsure which foot to use after making room on the right, before poking his effort wide.
The Danes may have been solid at the back for the first 45 minutes, but they slipped up straight after the restart to gift their opponents the lead.
The advantage could have been doubled after another mistake - this time from Simon Kjaer - saw Van Persie played in, but indecisiveness from the striker allowed Sorensen to swoop.
Coach Olsen then made his first change by introducing Jesper Gronkjaer, but it was the Oranje that continued to look dangerous.
Van der Vaart showed good skill in trying to cutely volley Van Persie's pass in, but Sorensen again intercepted.
Mikkel Beckmann and Christian Eriksen were also thrown on for Denmark, the former for Bendtner, but they still struggled to carve out any real openings although Agger struck a low shot into the gloves of Stekelenburg.
And Bert van Marwijk's team were always a threat going forward, with substitute Eljero Elia causing plenty of problems down the left.
Sneijder almost made it 2-0 eight minutes from time, but saw his 25-yard effort deflected onto the crossbar by Agger with Sorensen beaten.
However, five minutes from time Kuyt sealed the points. Elia's shot from the left was diverted onto the right-hand post by Stoke goalkeeper Sorensen and the Liverpool forward easily finished.
Netherlands: Maarten Stekelenburg, Gregory van der Wiel, John Heitinga, Joris Mathijsen, Giovanni van Bronckhorst (C), Dirk Kuyt, Mark van Bommel, Wesley Sneijder, Nigel de Jong (Academy De Zeeuw 88), Rafael van der Vaart (Eljero Elia 66), Robin van Persie (Ibrahim Afellay 76).
Denmark: Thomas Sorensen, Daniel Agger, Simon Kjaer, Lars Jacobsen, Simon Poulsen, Martin Jorgensen (C), Christian Poulsen, Thomas Enevoldsen (Jesper Gronkjaer 55), Thomas Kahlenberg (Christian Eriksen 73), Dennis Rommedahl, Nicklas Bendtner (Mikkel Beckmann 61)