The Americans Coco Gauff and Jessica Pegula were also big winners, ensuring that normal order was resumed on day five at Melbourne Park following the shocks of a day earlier.
World number two Ons Jabeur was the biggest casualty in the women's draw on Thursday, while the men's field has lost its top two seeds in Rafael Nadal and Casper Ruud.
Hot favourite Swiatek, a three-time major winner but chasing a first Australian Open title, swatted aside qualifier Cristina Bucsa of Spain 6-0, 6-1.
The Pole faces Elena Rybakina next after the Wimbledon champion defeated last year's Melbourne runner-up Danielle Collins in three sets. "For sure she's very strong physically and mentally," Moscow-born Kazakh Rybakina said, eyeing up the Swiatek challenge. "I will have to take all my chances.