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The world number one extended her extraordinary winning run to 32 consecutive matches but she did not have it all her own way in a 6-7 6-0 6-2 victory over the Chinese teenager.
Zheng was 3-0 down in the first set in no time at all but battled back superbly before saving five set points to take the opener herself, as Swiatek lost a set for the first time in more than a month.
A thigh injury limited Zheng from that point onwards though and Swiatek, who turns 21 on Tuesday, cruised through the rest of the match to continue her bid for a second Roland Garros title and set up a quarter-final match against 11th seed Jessica Pegula.
“I’m happy I could come back after a pretty frustrating first set, when I had the lead,” Swiatek said. “Just proud of myself that I’m still in the tournament.
“Quarter-final is such a stressful round so hopefully I’m going to be able to play my game and be loosened up.
“I know how Jessica can play, she’s had such a great season. She’s a pretty dangerous opponent so I hope I’m going to play my tennis, be focussed and I think it’s going to be OK.”
Pegula herself had to come from a set down as she beat Irina-Camelia Begu 4-6 6-2 6-3 earlier on Monday. She faces the toughest test in women’s tennis right now against Swiatek, who beat her in straight sets last month in Miami.
Madison Keys fell short in her bid for a third French Open quarter-final appearance as Veronika Kudermetova beat the American 1-6 6-3 6-1 in a topsy-turvy encounter. Kudermetova will face Daria Kasatkina in the last eight after the 20th seed breezed past Camila Giorgi.
On the men’s side of the draw, the two biggest names in the bottom half of the draw crashed out.
Second seed Daniil Medvedev, in just his second tournament back from a hernia operation, had been impressive in his first three matches at Roland Garros but that all came crashing down against Marin Cilic.
The world number two failed to earn even a single break on the Cilic serve across the three sets, as the 2014 US Open champion cruised to a 6-2 6-3 6-2 win over Medvedev.
It remains to be seen what comes next for Medvedev, who is unable to compete at Wimbledon next month due to the ban on Russian and Belarusian players. He could, however, still become world number one after the tournament, as a result of the tournament being stripped of ranking points and the impact that will have on Novak Djokovic.
Cilic will face Andrey Rublev in the quarter-finals, who was 1-6 6-4 2-0 up against Jannik Sinner when the Italian retired with a knee injury.
Fourth seed and 2021 French Open finalist Stefanos Tsitsipas was also sent packing as he was beaten in four sets by Holger Rune.
The 19-year-old from Denmark arrived in Paris having never previously won a main-draw match at a Grand Slam, but he put that record to bed with a first-round victory over Denis Shapovalov.
This was Rune’s most impressive victory to date though, beating Tsitsipas 7-5 3-6 6-3 6-4 to move into the last-eight.
“I was very nervous, but at the same time I knew that if I went away from my tactics I would lose for sure,” Rune said after the match.
“It was part of the tactic to be as aggressive as possible - Tsitsipas attacks every ball so I had to be aggressive, play fast and I really like playing the drop shots. It worked out and I’m really happy.”
Rune, who won the junior title at Roland Garros three years ago, faces Casper Ruud next after the eight seed reached the quarter-finals of a Grand Slam for the first time. He beat Hubert Hurkacz 6-2 6-3 3-6 6-3 on Suzanne Lenglen.