Yeats appeared to have won earlier in the match when she grabbed her opponent by both legs and just started spinning her around.
However, after the judges took another look at the sequence, they decided she did not earn enough points to win, so the match continued.
It ended when Yeats got the three points she needed to increase her lead to double digits (a level called "technical superiority"), which is one of the ways to win a match in freestyle wrestling.
The other way is to have the most points at the end of the six-minute match (made up of two three-minute periods).
In Yeats's two other matches, she won 6-0 and 14-3.
The 21-year old was a gymnast until she was 14, when she switched to wresting, a sport that runs in her family. Her father, Doug Yeats, went to five Olympics as a Greco-Roman wrestler.
Yeats herself is a nine-time national champion, and in 2014 she won gold at the Commonwealth Games in Glasgow.
On Friday night, she was not the only Canadian wrestler to reach the podium. In the women's 63-kg class, Braxton Stone-Papadopoulos also won gold, defeating Katerina Vidiaux of Cuba 7-3.
In the women's 75-kg division, Justina Distasio came away with the silver after losing a close final match 7-6 to American Adeline Gray, ranked No. 1 in the world.
Canada added a fourth medal, a bronze won by two-time Olympian Haislan Garcia in the men's 65-kg freestyle.