The world number ones twice came from behind to force golden goal extra-time but that could not separate the teams.
It went to the shoot-out and after Naomi van As and Eva de Goode had scored, Ellen Hoog netted the winner with only Stacey Michelsen converting from four New Zealand attempts.
The Netherlands had to work hard for their victory but heading into the final they will be comforted by the return to form of captain and penalty corner specialist Maartje Paumen, who struck twice - the second a trademark powerful flick.
New Zealand, who finished last in Beijing and were in their first Olympic semi-final, had first gone ahead through Kayla Sharland's early corner and then Krystal Forgesson.
The best chance in golden goal extra-time also fell to Paumen but she flicked a penalty corner inches wide five minutes from the end.
Max Caldas, coach of the Netherlands, saw more positives in the result than his side's actual performance.
'I think it was a game that had everything, from great goals and big misses, penalty corners and a shoot-out,' he said. 'The crowd had a great day and got their money's worth.
'We came out on top but at times we were lucky and at times we were unlucky. Today we chose to climb a mountain but we chose to climb it the wrong way: not the shortest way but the most difficult.
'I am disappointed about the game but not the result because I am happy we have a chance to win a medal.'