Lin, who together with Algerian boxer Imane Khelif is at the centre of a storm over their eligibility, defeated Bulgaria's Svetlana Staneva on a unanimous points decision to reach the semi-finals of the women's 57kg category.
With her second win of the tournament, the 28-year-old Lin is certain to win a medal because losing semi-finalists in the boxing take home bronze.
After a scrappy and tetchy fight, the 34-year-old Staneva made an X sign with her fingers to the crowd and, clearly angry, declined to speak to reporters.
But her coach Borislav Georgiev held a piece of paper with the words: "I'm XX. Save woman sport."
In most cases, males have both an X and Y chromosome, while females have two X chromosomes.
Khelif, who boxes again on Tuesday, is also guaranteed at least bronze after winning her quarter-final on Saturday in the women's 66kg division.
Khelif and Lin were disqualified from last year's world championships after failing gender eligibility tests, but were cleared to box in the French capital.
They also competed at the Tokyo Games in 2021 but did not win medals.
Neither boxer is known to identify as transgender.
Lin will face Turkey's Esra Yildiz Kahraman on Wednesday in the semi-finals.
The Taiwanese said she appreciated the support from people back home, where she has had the public backing of the government and fans.
"I just know that everyone is cheering for me and I know that all the people in Taiwan are behind me and support me," she said.
The controversy ignited on Thursday when Khelif needed just 46 seconds to win her opening bout in the French capital, forcing an abandonment against her hurt and tearful Italian opponent Angela Carini.
Carini, who suffered a badly hurt nose and was distressed, collapsed to the centre of the ring in tears.
Lin and the 25-year-old Khelif were disqualified from the 2023 world championships, run by the International Boxing Association (IBA).
The boxing in Paris is organised by the International Olympic Committee (IOC), which took over because of governance, financial and ethical issues at the IBA.
The IOC has leapt to the defence of Khelif and Lin, with president Thomas Bach on Saturday saying they were born and raised as women, and have passports saying that.
