The match finished 1-1, but Canada won 3-2 on penalties, meaning Quinn and Canada won gold. Quinn had won a bronze medal at Rio 2016 when Canada beat Brazil, but they did not come out until September 2020.
They made history as the first openly transgender athlete to compete at an Olympic Games when they competed in Canada's opening match against Japan, which ended in a 1-1 draw following goals from Christine Sinclair and Mana Iwabuchi.
"First openly trans Olympian to compete. I don't know how to feel. I feel proud seeing 'Quinn' up on the lineup and on my accreditation," Quinn said in a statement released through the National Women's Soccer League's social media at the time.
"I feel sad knowing there were Olympians before me unable to live their truth because of the world. I feel optimistic for change. Change in legislature. Changes in rules, structures and mindsets.
"Mostly, I feel aware of the realities. Trans girls being banned from sports. Trans women facing discrimination and bias while trying to pursue their Olympic dreams. The fight isn't close to over ... and I'll celebrate when we're all here."
Quinn plays with OL Reign in the NWSL when not on international duty with Canada.
The North American side made it to the Olympic soccer final after beating the United States women's national team 1-0 in the semifinals. The win marked the first time since 2001 that Canada secured a victory over their continental rivals.
Quinn was not the only transgender athlete to compete at the Games, with weightlifter Laurel Hubbard also appearing.
It was a difficult tournament for her, as she missed all three of her snatch attempts in the women's +87 kilogram category.
"I haven't come here to change the world. I've come here because sport is part of me," Hubbard said.
"I haven't set out to look for special accommodation or treatment or anything else.
"The IOC has tried to put in place regulations that apply to all sports. I suspect over time there will be more refinement ... but it's not my area of expertise."