The world series champions went behind early in the match but unanswered tries from Emma Tonegato, Evania Pelite, Ellia Green and Charlotte Caslick gave them a lead New Zealand were unable to overhaul.
The Australians huddled in tearful hugs under the posts at the realisation their dream, not only of having the chance to compete in the Games but of winning gold, had been realised.
"It brings tears to my eyes," explained Green.
"We've just made Australian history, rugby history. It means everything."
New Zealand, who had two tries from the outstanding Kayla McAlister and one at the death from Portia Woodman, performed a tearful haka in front of the crowd at the end of the match, their dreams of gold shattered.
"Pretty gutted. We came out here to win a gold medal and we are bringing back a silver," said New Zealand captain Sara Goss.
"But silver's still good in New Zealand's eyes and we hope we have done them proud."
It was the spell around halftime that Woodman, the top try scorer in the tournament with 10, spent in the sin-bin for a deliberate knock-on that probably ended New Zealand's hopes.
Without question the best two of the 12 teams in the tournament, both New Zealand and Australia had come through scares at the hands of the United States on Sunday to stamp their authority on the semi-finals.
After a tight and physical start to the final, McAlister forced her way over in the corner for her sixth try of the tournament to give New Zealand an early lead before Tonegato hit back with her seventh.
Australia had started to find holes in the New Zealand defence and when Woodman was sent off for two minutes, first Pelite then speedster Green benefited from the extra space to give the women in green and gold a 17-5 lead just after halftime.
Charlotte Caslick then nipped over for another converted try to further extend Australia's lead and although McAlister grabbed her second try, two converted scores for New Zealand in little more than a minute was always going to be a big ask.
Woodman did finally weave her way over to score under the posts but the hooter had sounded and Australia were already well into their celebrations when Tyla Nathan-Wong took the conversion.
Canada earlier took the bronze with a 33-10 victory over Britain. [nL4N1AP4H7]
Rugby was last included at the Olympics in Paris in 1924 when the United States beat hosts France in the final of a men's 15-aside tournament.
Australia coach Tim Walsh said he thought the inaugural women's tournament had shown the sport deserved its place at the Games.
"We certainly up held the values of the Olympic movement, and rugby," he said. "I think we have created a very sustainable future for rugby sevens at the Olympic Games."
(Editing by Greg Stutchbury)
