The world No.2, who was playing her first match since her semi-final loss to American Madison Keys at Melbourne Park, dispatched Greece's Maria Sakkari 6-3 6-2 in just 84 minutes.Â
Swiatek's win extended her winning run to 14 matches at the tournament as she bids for an unprecedented fourth-consecutive title.
"Honestly, hard to say," said the 23-year-old Pole when quizzed about what suits her game at the Khalifa International Tennis and Squash Complex.
"Every year it's different, every year there is a different story, so it's hard to compare and hard to find one thing that worked exactly.
"From what I remember it's not like I've been playing flawlessly, so it's not like these tournaments were perfect, but at some point always I found some solutions. I think the conditions here are pretty tricky, and I was patient enough to just keep focusing on my game."
The ninth and 10th seeds also progressed on Tuesday (AEDT).
Spain's Paula Badosa won a three-setter over Renata Zarazua of Mexico, while Daria Kasatkina bageled fellow Russian Polina Kudermetova.
Canada's Layla Fernandez joined Swiatek in round three by defeating eighth seed Emma Navarro of the US, and 15th-seeded Croatian Donna Vekic also failed to advance.
Sofia Kenin, Ons Jabeur and Elina Svitolina were also victorious.
Top seed Aryna Sabalenka, who was upset by Keys in the Melbourne decider, begins her campaign against Ekaterina Alexandrova on Wednesday.