Top seed Swiatek, 23, broke serve in the first game of the match and, apart from briefly losing serve in the second set, retained control to win 6-2 6-4.
Third seed Gauff saved three match points before Poland's Swiatek closed out victory.
The 20-year-old American has now lost 11 of her 12 matches against the world number one.
She could join Monica Seles (1990–1992) and Justine Henin (2005–2007) as the only women to win three straight French Open women's titles during the Open era.
She will face Italian 12th seed Jasmine Paolini or unseeded 17-year-old Russian Mirra Andreeva in Saturday's final.
Paolini, 28, and Andreeva meet in the second semi-final later on Thursday.
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