Świątek, the world number eight, beat Bouzkova 7-6 (7-3), 7-6 (7-3), winning both sets in tie-breaks after saving three set points in the second.
The 25-year-old Pole said she tried to treat those moments like any other point to avoid piling on extra pressure, adding that staying focused let her concentrate purely on her own game rather than the score.
Świątek praised Bouzkova's variety, noting the Czech's long rallies and slices sometimes forced her to retreat rather than move forward as she would have liked.
The Polish player said winning such tight contests boosts confidence, though she stressed every match is different and requires patience and readiness for opponents.
Świątek leads Zheng 7-1 in their head-to-head record, with the Pole's only defeat coming in their semi-final at the 2024 Paris Olympics.
The Chinese player reached the fourth round by beating 22nd seed Madison Keys of the US 1-6, 7-6 (7-3), 7-5, saving a match point after trailing 0-5 in the decider.
Świątek, the 2022 US Open champion, is seeking her seventh Grand Slam singles title in New York.
She is the last Polish singles player remaining in the tournament after countrywomen Maja Chwalińska, Magda Linette and Magdalena Fręch all went out in the first round.
On the men's side, Poland's Hubert Hurkacz and Kamil Majchrzak were both eliminated in the second round.
The 2026 US Open runs until September 13.
(ał)
Source: PAP