The Scandinavians picked up an early lead against the World Cup finalists and, although they fell behind shortly after the break, eventually recorded a crucial victory
Kim Kallstrom opened the scoring after 15 minutes of play before Klaas-Jan Huntelaar restored parity halfway through the first half. Dirk Kuyt gifted the Dutch the lead shortly after the interval, but Sebastian Larsson and Ola Toivonen helped Sweden to the crucial three points.
Sweden got a free kick in a dangerous position in the 15th minute after Jeffrey Bruma fouled Johan Elmander on the edge of the box and Lyon midfielder Kim Kallstrom showed his class with a superbly curled shot over the wall and into the top corner to open the scoring.
Nevertheless, Holland wasn't too impressed and Klaas-Jan Huntelaar restored parity halfway through the first half. Erik Pieters sent in a perfect cross from the left and the Schalke man beat his marker to the ball before finding the net with a superb header.
Netherlands started the second half brilliantly and grabbed the lead in the 50th minute. Rafael van der Vaart set up Van Persie with a superb pass and the Arsenal star tried his luck with a good volley. Andreas Isaksson managed to keep Van Persie's shot out, but Dirk Kuyt was alert and headed home from close range to make it 2-1.
The hosts immediately leveled the scoring again though after the referee awarded them a spot kick in the 51st minute following handball from Joris Mathijsen. Sebastian Larsson stepped up to take the penalty and beat Michel Vorm with a low shot in the left corner.
Sweden took advantage of the Dutch's lack of concentration once more in the 54th minute. Johan Elmander went past Mathijsen down the right before laying the ball off for Toivonen, who fired home from inside the area.
Huntelaar almost scored his 31st goal of his international career after a corner from the left, but his superb header was parried by Isaksson.
A superb free kick from Elm almost surprised Vorm between the sticks, but the Swansea shot stopper realized just in time what the AZ star had in mind and tapped his shot over the crossbar.
Sweden finishes second in Group E following Tuesday's victory with 24 points from 10 games and qualifies for next year's tournament as the best runner-up.
Netherlands has lost its perfect record, but will still be quite pleased with its qualifying campaign as it recorded nine wins and one loss to book its ticket for Euro 2012.