The five-time Grand Slam champion eased to a 6-4, 6-4 success over fellow former world number one to reach the quarter-finals.
Swiatek, whose three-year French Open reign was ended in the semi-finals by Aryna Sabalenka earlier this month, will next face either Maria Sakkari or Ekaterina Alexandrova.
The 24-year-old has never reached the final of a grass-court tournament before.
Her best performance at Wimbledon, which starts on Monday, was a run to the 2023 quarter-finals.
Another former world number one was in action later in the day as Japan's Naomi Osaka fell in straight sets to fifth seed Emma Navarro.
Four-time Grand Slam winner Osaka, now ranked 56th in the world after returning from maternity leave last year, went down 6-4, 6-4 against her American opponent.
Navarro advanced to play her compatriot, the top seed Jessica Pegula in the quarter-finals.
World number three Pegula dispatched 78th-ranked Czech Katerina Siniakova 6-2, 6-3 in just over 65 minutes.
Last year's Wimbledon runner-up Jasmine Paolini of Italy booked her spot in the last eight with a battling 7-6 (10-8), 7-6 (8-6) win over Canadian 2021 US Open finalist Leylah Fernandez.
The second seed will next face Ukrainian Elina Svitolina or Brazilian Beatriz Haddad Maia.