Netherlands took control from the start of extra-time and in the 99th minute, Jackie Groenen found space outside the box and the midfielder fired a low strike into the bottom corner.
Netherlands are facing Sweden in the Women's World Cup semi final tonight.
US edged England 2-1 on Tuesday in a classic semifinal.
The Netherlands have always been a force in the men's game, but they had never even been to a major women's tournament until a decade ago.
Coverage of the match begins here on FOX 13 at 8:00 a.m. with FIFA Women's World Cup Live.
It was a simmering second half right from the onset as both teams realised that a solitary goal could very well be the difference.More news: Megan Rapinoe says she’s ‘uniquely and very deeply American’
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But it was only in the second half that the Dutch fans had much to shout about, Vivianne Miedema forcing Sweden's goalkeeper, Hedvig Lindahl, into a fingertip save which rattled the crossbar only minutes after Sweden's Nilla Fischer had hit the post with a long-distance daisy-cutter.
In the end it was a case of ideal timing for Netherlands midfielder Jackie Groenen.
"In extra time I felt we had more energy than they had and than got us through".
Questions over whether they are arrogant may still linger, particularly if joint-leading tournament scorer Alex Morgan breaks out another cheeky goal celebration as she did against England. We had more control and they had some chances, but we have a good goalkeeper in Sari and she made some really nice saves. The U.S. had a few injuries among their forwards, as did the Netherlands.
The Manchester United midfielder smashed home a fine effort from 20 yards out to give the Netherlands the lead. Immediately, her teammates sought her out and her pace put Sweden's defense on its heels.
Stina Blackstenius scored the winning goal in both knockout-round games, becoming just the second Swede - and the first since 1991 - to score in consecutive Women's World Cup knockout-round games.
As recently as five years ago, the Netherlands had never taken part in a Women's World Cup. "We have a team working on all these aspects, looking into everything", Gerhardsson said, according to The Associated Press. "I really believe in the medical staff".