The Swedes picked up an early lead against the World Cup finalists and have booked their place in Poland and Ukraine after qualifying as the best group runners-up
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 qualify as the best group runners-up.
The away side started the match with attacking intentions, but struggled to really trouble Sweden in the opening stages of the game. The hosts on the other hand appeared to be happy to sit back and tried to hit Netherlands on the counter-attack.
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 Kallstrom showed his class with a superbly curled shot over the wall and into the top corner to open the scoring.
Nevertheless, Holland weren't too impressed and 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.
Ola Toivonen got a good chance for Sweden to make it 2-1 after a long throw from Rasmus Elm, but the PSV star aimed just too high. Robin van Persie came close for the World Cup finalists, but the forward's right footed shot went inches wide.
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 Kuyt was alert and headed home from close range to make it 2-1.
The hosts immediately levelled the scoring again though after the referee awarded them a spot kick in the 51st minute following handball from Joris Mathijsen. 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 realised just in time what the AZ star had in mind and tapped his shot over the cross-bar.
Sweden finish second in Group E following Tuesday's victory with 24 points from 10 games and have qualified for next year's tournament as the best runner-up.
Netherlands have lost their perfect record, but will still be quite pleased with their qualifying campaign as they recorded nine wins and one loss to book their ticket for Euro 2012.