Swiatek, who dropped a single game in her previous match at the US Open tune-up event, needed time to work out Zheng but once she did she immediately looked more like the player who has occupied top spot in the world rankings since April 2022.
The Pole looked unsettled as Zheng jumped out to a 3-0 double-break cushion in windy conditions and the Chinese number one refused to let up as she broke for a third time to grab the first set when the Pole sent a forehand long.
Swiatek swapped her white outfit for a black one and it led to an instant change in her fortunes as she showed more conviction in her strokes and broke Zheng to love three times for a 5-0 lead en route to forcing a decider.
Swiatek motored through the final set and again feasted of Zheng's serve, breaking twice for a 5-0 lead before closing out the contests on her serve when her opponent sent a forehand long.
"Honestly, it's because of my coach," Swiatek said about her outfit change. "He told me a couple months ago that after losing a set it might be a good idea to change your outfit so you can kind of reset and go into the second set in a different vibe.
"I thought this was a bad (idea) but I tried this time and it worked, so thank you coach."
Awaiting Swiatek in the next round will be Vondrousova, who converted four of five break points during a 7-5, 6-3 victory over Sloane Stephens (30).
In other early action, world number four Elena Rybakina (28) was leading her match against Jasmine Paolini (27) 6-4, 2-5 when she retired, sending the Italian qualifier into the final eight.
Greek eighth seed Maria Sakkari (28) was knocked out with a 3-6 6-2 6-3 defeat over Czech Karolina Muchova (26).
