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The Spaniard beat Francisco Cerundolo 6-4 6-3 3-6 6-4 in the first round.
Djokovic and Nadal find themselves in different halves of the draw and they cannot face each other until the men's final on July 10.
Swiatek lost just one set during this year's Roland Garros campaign, extending her winning run to 35 matches.
The World No 1 had triumphed at Roland Garros in 2020.
World No. 1 Swiatek crushed her Russian opponent 6-2, 6-1 while teenager Gauff recorded a comfortable 6-3, 6-1 win over Trevisan in the semifinals.
Swiatek, who turned 21 on Tuesday, is on the longest unbeaten run in the women's tour since Serena Williams.
Djokovic defeated Tsitsipas 6-0, 7-6 for his first title of 2022.
Swiatek also became the first woman to win the opening three WTA 1000 tournaments in a season.
Results 51-58
