Erik Hamren's men 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 before Klaas-Jan Huntelaar restored parity midway through the first half. Dirk Kuyt gave the visitors the lead shortly after the interval, but Sebastian Larsson and Ola Toivonen helped Sweden to all three points.
Netherlands started the match with attacking intentions, but struggled to really trouble the hosts in the opening stages of the game.
Sweden won a free kick in a dangerous position in the 15th minute after Jeffrey Bruma fouled Johan Elmander on the edge of the box and Kallstrom showed his class with a superbly curled shot over the wall and into the top corner.
Nevertheless, Holland fought back and Huntelaar restored parity midway 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.
Toivonen had a good chance to make it 2-1 for Sweden 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 shot went inches wide.
Netherlands began 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 kept Van Persie's shot out, but Kuyt was alert and headed home from close range to make it 2-1.
The hosts immediately levelled matters 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 Holland'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 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 reasonably pleased with their qualifying campaign as they recorded nine wins and one defeat to book their ticket for Euro 2012.