Elsewhere, eighth seed Amanda Anisimova made it safely through to the second round by beating Australian Kim Birrell 6-3 6-2.
American Anisimova, playing her first Grand Slam match since being beaten 6-0 6-0 by Swiatek in the Wimbledon final, hit 17 unforced errors in the opening set but improved markedly in the second.
She won the last five games of the match to set up a second-round meeting with another Australian, teenager Maya Joint.
However, her compatriot Danielle Collins made an early exit for the second consecutive year, winning just two games as she was beaten by Jacqueline Cristian of Romania.
World number 50 Cristian prevailed 6-2 6-0 against 2019 Australian Open semi-finalist Collins, who was hampered by a back injury.
Meanwhile, two-time champion Naomi Osaka – seeded 23rd – cruised past Belgium’s Greet Minnen in a 6-3 6-4 win.
Russian Diana Shnaider, the 20th seed, also went out after Germany’s Laura Siegemund secured a 7-6 (7-3) 2-6 6-3 victory over the 21-year-old.
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