Neither side managed to find a way through in the regulation 90 minutes despite the woodwork being struck twice, but recent Manchester United addition Groenen finally found the mark to set up a final against the United States on Monday (AEST).
The respective defences generally came out on top in the first half, as neither team particularly captured the imagination when on the front foot, providing a stark contrast to Wednesday's semi-final contest between USA and England.
Proceedings opened up more after the break and both sides were denied by the frame of the goal, but it took until extra-time for the decisive goal to arrive, with Groenen producing a fine finish to seal a first ever World Cup final for her side.
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