After the scores were level at 1-1 at the end of normal time, the Dutch edged the shoot-out 4-3 and will face either New Zealand or Great Britain for the gold medal.
Ellen Hoog scored the winning goal in the shoot-out.
"At first I had some doubts because I missed the first shot, but I trust in my own shoot-outs so I thought, 'Well, I'm not going to miss it twice'," said Hoog who missed her first attempt.
"So I trust and I felt that the team trusted me as well, but after I scored it, I don't know what was going on. The most feeling I think is relief. Just relief that we won today."
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Germany were the last team to defeat the Netherlands at the Olympics on their way to the 2004 title.
They looked on the cards to repeat that when Lisa Schutze gave them an 11th-minute lead with a penalty corner.
But Dutch skipper Maartje Pauman levelled also from the set piece five minutes later.
Pauman took her Olympics goal-scoring record to 18 overall and four in Rio.
The victory gives Alyson Annan, the Australian coach of the Dutch team, the chance to become only the second woman coach to win an Olympic title.
Annan won two golds as a player with Australia in 1996 and 2000.
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