But after world No.74 Zheng had a medical timeout for a right thigh injury at 3-0 down in the second set, the world No.1 pulled away for a hard-earned victory after two hours and 45 minutes.
Swiatek, who is into her third straight Roland-Garros quarter-final, will play American Jessica Pegula, the No 11 seed, in the last eight.
Story of the match
Zheng had beaten Simona Halep on her way to round four of a Grand Slam for the first time and right from the start, Swiatek could tell that she would have to be on her toes. And so it proved as the 19-year-old gave her a huge scare.
With a big forehand and a backhand reminiscent of Li Na, China’s first and to date only Grand Slam singles champion, Zheng forced two break points in the opening game.
But Swiatek saved both, the first with a thunderous forehand winner and then broke in the next game before holding again to lead 3-0.
In her run of 31 straight wins, Swiatek had handed out 15 bagel sets but Zheng avoided that in the opening set with a superb serve-and-volley combination and then, with her confidence rising, broke Swiatek to get back on serve with a series of big-hitting groundstrokes.