Canada, home to the majority of the world's curlers, could make it a double on Friday when their men play Britain in the final. No country has won both gold medals at an Olympics.
Led by skip Jennifer Jones, Canada beat Sweden 6-3 to avenge a bitter defeat in the final in Vancouver four years ago when they had looked set for gold.
Jones was not part of that team, having missed out on selection for the last two Olympics.
"I don't think the magnitude of it has really sunk in yet. It's been so emotional," said Jones, a lawyer by profession.
"We are Olympic gold medallists, it is something that you dream of your entire life. It is what every athlete wants to do and we did it."
Canada are the first women's team to win an Olympics with a perfect record. Their men's team did it in 2010.
Canada had overpowered Sweden 9-3 in a preliminary group game last week but this was a much closer encounter and was all square until the closing stages.
The Canadians took a 4-3 lead in the eighth end thanks to a tight decision using the measuring gauge to decide whether theirs or the Swedish stone was closest to the target.
They added a further two points in the ninth end when Sweden suffered from a bad bounce and made a couple of errors. Jones hopped with delight as her last stone helped take her team closer to the Olympic title.
"The ninth end was not good," said Swedish coach Fredrik Hallstroem, pinpointing the contest's pivotal moment.
"They played a little bit better than us on the important shots. It's two strong teams, it can go either way, they were a bit ahead of us."
Britain beat Switzerland earlier to claim the bronze medal. The British team, with an average age of 23, are the youngest to win a curling medal.
With the men's team guaranteed at least a curling silver, Britain are certain to equal their best Winter Olympics haul of four medals.
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