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The 18-year-old beat Swiss opponent Viktorija Golubic 6-4 6-1 in a final contested by two qualifiers, achieving her breakthrough win in an hour and 29 minutes.
Golubic saved five match points but eventually was put away by Tauson, who has spent most of her senior career to date on the second-tier ITF tour.
She caused a major shock at the French Open in September by beating US Open semi-finalist Jennifer Brady in the first round, and Tauson should now become a more familiar presence at the higher level.
The win carries the youngster into the WTA top 100 for the first time, and it completed an impeccable trip to France that saw Tauson win all seven of her matches, including two qualifying rounds, in straight sets.
She said of her performance: "I think I've been really solid; especially after the first set, I've come out good in every single match."
Quoted on the WTA website, Tauson added: "I just kept my game going. It's been a weird week like that, normally I have some fall-outs, but I haven't had any of those this week, so I'm very happy with that."
Tauson shocked Russian top seed Ekaterina Alexandrova in the first round at the start of the week in Lyon, and Alexandrova lost to another teenager on Sunday as the Dubai Tennis Championships began.
The world number 33 was handed a tough draw against American Coco Gauff, who scraped through 7-6 (7-3) 2-6 7-6 (10-8) in a match lasting two hours and 41 minutes.
Gauff served 12 double faults, including seven in the deciding set, but found a way through to the second round.
Svetlana Kuznetsova, Ons Jabeur and Alize Cornet were among the other winners on day one. The top eight seeds, who include Iga Swiatek, Karolina Pliskova, Elina Svitolina and Petra Kvitova, have all received byes to round two of the WTA 1000 event.