The Pole led 5-0 in the first set and held set points, before losing seven games in a row to hand Zheng the opener.
It was a repeat of their dramatic Paris Olympics semi-final two years ago, when the Chinese player also came from behind to beat Świątek.
The match lasted one hour and 53 minutes.
Świątek was 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: IAR