Great Britain's Hannah Mills and Saskia Clark, who entered the medal race top of the standings alongside them, took silver.
The Netherlands pair of Lisa Westerhof and Lobke Berkhout took bronze after coming sixth in the medal race.
With light winds playing havoc on the south coast, only two flights were possible on the Nothe Course for the women's Eliot 6m match racing before the breeze died.
Racing was postponed and moved to Portland Harbour, where it restarted at 5pm with both semi-finals tied at 1-1.
With no racing able to take place after 5.30pm, the third flight became decisive and Olivia Price-skippered Australia beat Silja Lehtinen's Finland on a photo finish after a superb comeback.
Price said: 'It really was a hard fight, we had to make some really good decisions and we got there in the end. To be honest I'm still trying to take it all in.'
Australia will face Spain for the gold medal after Tamara Echegoyen's team overcame Ekaterina Skudina's Russia in the final race of the day.
Echegoyen said: 'Now we fight for gold.'I think it will go to five races. The Australians sail very well and we will have to fight a lot. I think all the races will be close.
'I think the secret is that we have sailed with great concentration and calm, and I think the favourites have the pressure.'
As well as the gold medal race, Finland and Russia will fight for bronze tomorrow.