The 21-year-old Pole, who won last year's Indian Wells, had match point at 6-0 5-0, before Liu rallied back on serve to avoid the ignominy of a double-bagel defeat, with Swiatek eventually winning 6-0 6-1.
Swiatek was in a dominant mood, winning 57 of 83 points for the match and converting five of nine break points generated. She dropped only 11 points in seven service games.
The three-time grand slam champion is 13-3 on the season, with all 13 wins coming in straight sets. In five of those matches, she has dropped just one game.
Former US Open winner Emma Raducanu moved into the third round with a 7-6 (7-3) 6-2 win over 20th seed and 2023 Australian Open semi-finalist Magda Linette.
Raducanu's win meant she has put together back-to-back victories for the first time since September, setting up a clash with 13th-seed Beatriz Haddad Maia after she beat Katerina Siniakova 5-7 7-6 (7-4) 6-3.
Fourth seed Ons Jabeur fought back from a set down to prevail over Magdalena Frech 4-6 6-4 6-1 in one hour and 44 minutes.
Former US Open champion Bianca Andreescu also overcame an early deficit to win 4-6 6-4 6-3 over Peyton Stearns.
Reigning Wimbledon champion Elena Rybakina got the edge in a tight two-set clash with 2020 Australian Open winner Sofia Kenin, triumphing 7-6 (8-6) 7-6 (7-5) in two hours and 10 minutes. Rybakina fought back from 4-1 down in the second frame.
Fifth seed Caroline Garcia overcame a wobble to win 6-1 6-7 (4-7) 6-4 over Hungary's Dalma Galfi, with 30th seed Leylah Fernandez her next opponent after beating Emma Navarro 6-2 6-4.
Two-time major winner and three-time US Open finalist Victoria Azarenka was the big casualty from the day's play, losing 7-6 (7-1) 6-3 to 2021 Australian Open semi-finalist Karolina Muchova.
Swiatek started shakily as her serve was broken in the first game of the match, and although she got it back instantly, both competitors ended up creating eight break point opportunities each in a closer-than-expected match.
She will meet England's Emma Raducanu in the fourth round after the resurgent 20-year-old collected her best win of the year, defeating 13th seed Beatriz Haddad Maia 6-1 2-6 6-4.
Raducanu, the 2021 US Open champion, has begun to work her way back up the rankings. Having come into the tournament ranked 77th in the world after an injury-riddled season, she has now won four of her past five matches, with her only loss in that span coming against world number six Coco Gauff at the Australian Open.
World number five Caroline Garcia was pushed to a third set for the second match in a row, but prevailed 6-4 6-7 (7-5) 6-1 against Leylah Fernandez, booking a clash against Romania's Sorana Cirstea after she won 6-3 6-1 against fellow unseeded competitor Bernarda Pera.
Karolina Muchova kick-started a great day for the Czech Republic representatives as she got the better of Italy's Martina Trevisan 6-4 3-6 6-4, and Marketa Vondrousova kept it going with a 7-6 (7-5) 6-4 victory over world number four Ons Jabeur.
Reigning Wimbledon champion Elena Rybakina is shaping up as a threat to win it all, yet to drop a set this week following her 6-3 7-5 triumph over Paula Badosa.
The French top seed looked to be in trouble as Belgian Van Uytvanck eased to the first set, before Garcia found her feet to come back and overwhelm her opponent 2-6 6-0 6-1.
She will face Jasmine Paolini in the last eight after the Italian took just over an hour to dispose of Erika Andreeva 6-2 6-3.
Second seed Zhang Shuai is out though after falling to another Belgian in Maryna Zanevska 6-2 6-0.
Fifth seed Anastasia Potapova will face Zanevska next after her 6-4 4-6 6-3 win over Clara Burel, while seventh seed Danka Kovinic is also through after beating Anna Bondar 4-6 6-2 6-3.
At the Thailand Open, top seed Bianca Andreescu had no problems against Anastasia Zakharova, easing through to the quarter-finals 6-2 7-5.
The Canadian will face Marta Kostyuk next after the Ukrainian fifth seed defeated Nao Hibino 6-3 7-6 (9-7).
Sixth seed Tatjana Maria also progressed 6-0 6-4 against Dayana Yastremska, as did Heather Watson as she fought hard to see off Han Na-lae 6-3 5-7 6-4.
World number 115 Beatriz Haddad Maia of Brazil stunned Pliskova in straight sets to reach the round of 16 at a WTA Premier 1000 event for the first time.
The 15th and 16th seeds, Gauff and Andreescu, also exited in two sets, albeit to seeded players.
LUCKY LOSER OUSTS PLISKOVA
Haddad Maia lost in the final round of qualifying but made the main draw as a lucky loser when Nadia Podoroska withdrew through injury, and she has made the most of that reprieve with a 6-3 7-5 defeat of the world number three.
She had faced Pliskova once before and it did not go well, a 6-1 6-1 rout at the 2018 Australian Open, but the Czech struggled to find her trademark serve amid powerful winds in the California desert.
Pliskova suffered 12 double faults and won just 43.4 per cent of points on her serve, whole Haddad Maia saved nine of the 14 break points she faced on her own serve.
KONTAVEIT STAYS HOT TO DETHRONE ANDREESCU
Haddad Maia next faces 18th seed Annett Kontaveit, who ousted Andreescu 7-6 (7-5) 6-3 to end the Canadian's dreams of a repeat.
Kontaveit has won 15 of her last 16 matches, winning titles in Cleveland and Ostrava during that stretch. Monday, she captured the first set on her fifth set point before rallying from a 3-1 deficit in the second to run the table and seal the win.
"It was extremely close throughout the match and I was just trying to stay tough. I was ready for a tough match," Kontaveit said. "She's such a good player, such a great competitor, so I knew it wasn't going to be over until it was really over."
BADOSA BOUNCES GAUFF
Paula Badosa, the 21st seed, breezed past Gauff 6-2 6-2 as the American teen also had trouble with her serve, hitting just two aces after recording 12 in her previous match.
In a meeting of the last two defeated finalists in the tournament, 10th seed Angelique Kerber beat 20th seed Daria Kasatkina 6-2 1-6 6-4.
Third seed Barbora Krejcikova handled Amanda Anisimova with ease, 6-2 6-3.
Ons Jabeur, the 12th seed, had little trouble in downing 22nd seed Danielle Collins 6-1 6-3.
Andreescu sustained the injury at the WTA Finals in Shenzhen in October, from which she withdrew after retiring in her match with Karoliona Pliskova.
The Canadian, who stunned Serena Williams in the final of the 2019 US Open, explained that she and her doctors decided she had not made enough progress in her rehabilitation to play at the year's first grand slam in Melbourne.
In a post on Twitter, she wrote: "Hey guys, just wanted to give you a little update on my knee rehab after I got injured at the WTA finals in Shenzhen.
"My rehab is going well, I feel better and stronger every day but after discussing it with my team and following the recommendation of the doctors, the Australian Open is unfortunately too soon in my rehab process and I sadly will not be able to play in it this year.
"It was a very tough decision to make as I love to play in Melbourne but I have to respect the recuperation plan for my knee and body. I can’t wait to come back to Aus soon."
Andreescu's incredible victory at Flushing Meadows was the highlight of a superb 2019 for the 19-year-old, which saw her rise to number four in the world. She has since dropped to number six.
The teenager also claimed glory at Indian Wells and the Rogers Cup and enjoyed a 17-match winning streak in which she did not lose a single completed contest, with a run that started in March finally ended by Naomi Osaka in October at the China Open.
Her withdrawal will remove a significant obstacle for defending champion Osaka, as well as the likes of Williams, Ash Barty and Simona Halep, as Andreescu focuses on her continued recovery and the French Open.
Aside from her run in New York, Andreescu has never gone beyond the second round of a major and will hope she is fit enough to change that fact at Roland Garros in May.
The Greek sealed a 6-7 (2-7) 7-6 (8-6) 6-3 victory in a gruelling last-16 clash that finally concluded at 02:13 local time in New York – the latest finish to a women's singles match in tournament history.
Sakkari saved eight of the 12 break points she faced as she racked up 46 winners and 40 unforced errors after adopting a bold approach to fight back from a set down and wrap up the victory in three hours and 30 minutes.
She ended 2019 champion Andreescu's 10-match unbeaten streak at the US Open and was delighted to see her tactics pay off, with Karolina Pliskova standing between her and second grand slam semi-final of the year.
Speaking about her fearless showing, Sakkari, who was beaten in the last four at Roland Garros, said: "It's something that I've been working with [coach] Tom [Hill] since end of last year, but I felt like I lost that bravery after the French. I was more hesitant. I was not going for it so much.
"After my loss [in Cincinnati] with Angie [Angelique Kerber] I just practiced for two weeks. I had some very tough practices where I was crying because I could not feel my shots, I could not feel my tennis. But thankfully I had Tom and Yannis, my hitting partner, that supported me a lot.
"I lost my identity. That's how I called it. I lost myself, part of myself. With my psychologist, as well, I found a way to come back and feel again what I felt out there today.
"By telling myself to be more brave, it's not like, Maria, now be brave, and you're brave. It's just a process in practice and everything that has helped me to be more brave.
"I mean, there was a decent crowd staying until 2:30 at night. I said, Maria, you cannot give up. Just stay focused and stay calm and just make balls."
The 30-year-old Watson lost in qualifying for the recent Australian Open, having made the singles main draw for 11 consecutive years, but she is already beginning to make up for the Melbourne disappointment.
Kazakh Putintseva is ranked 44th in the world, while Watson has slipped to 160th, but the Guernsey native has been as high as 38th in her career and won four titles on the WTA Tour.
She showed there is still a hunger to succeed, edging a tight contest 5-7 6-4 7-5 (7-5) to make Putintseva the biggest early casualty.
Top seed Bianca Andreescu had no such trouble against Watson's compatriot Harriet Dart, as the Canadian went through a 6-3 6-4 winner.
Czech 17-year-old Linda Fruhvirtova, seeded eighth and at a career-high 51st in the WTA rankings, overwhelmed American veteran Bethanie Mattek-Sands 6-3 6-1.
Fellow seeds Marta Kostyuk, Anna Kalinskaya and Tatjana Maria also came through their opening tests at the tournament in Hua Hin.
At the Lyon Open, French top seed Caroline Garcia fended off Czech Tereza Martincova 6-4 7-6 (7-4) in round one, delighting a home crowd.
Champion at the WTA Finals at the end of last season, Garcia surprisingly lost in round four of the Australian Open to unseeded Pole Magda Linette, who went on a fairy tale run to the semi-finals.
Garcia said of Tuesday's win over Martincova: "It was a tough match. She's a great player. She's already played great battles against top players, and it's a first round, so you really never know what is going to happen."
Second seed Zhang Shuai beat American Madison Brengle 6-3 6-2, but eighth seed Anna Blinkova bowed out, retiring when 4-0 behind in a deciding set against fellow Russian Erika Andreeva.
Two weeks on from losing to the same opponent on grass in Berlin, Andreescu suffered another straight-sets disappointment, going down 6-2 6-1.
The Canadian boasted a better first serve percentage (73 to 63) and hit more winners (17 to 11) but paid for a high unforced errors count (34 to seven) as she crashed out.
Andreescu's defeat extends a frustrating period since winning the US Open two years ago.
The 21-year-old, who recently split with long-time coach Sylvain Bruneau, has seen her career limited by a combination of injuries and the break enforced by the coronavirus pandemic.
As for Cornet, her Wimbledon campaign will continue with a second-round clash against either Greet Minnen or Ajla Tomljanovic.
The Frenchwoman is aiming to improve on the career-best run that saw her reach the fourth round at SW19 in 2014.
The Canadian 22-year-old was enjoying an excellent run in the tournament, knocking out Emma Raducanu, Maria Sakkari and Sofia Kenin en route to the last-16 stage.
She dropped the first set against Ekaterina Alexandrova but was an early break to the good in the second when injury struck, forcing her to abandon that fourth-round match.
Andreescu was so badly hurt she needed to be taken off court in a wheelchair, bringing an early end to Monday's match.
It remains to be seen how serious Andreescu's injury proves to be, and whether she faces a long lay-off.
She indicated on Tuesday that early tests had taken place and managed to make light of the situation.
In a post on Twitter, she wrote: "Woke up with a brace on my foot… anyone know what happened?"
"On a serious note tho… that was the worst pain I've ever felt… praying for nothing serious.
"Still waiting on official results. Thank you everyone for your thoughts and kind words, doesn't go unnoticed."
Andreescu won the US Open in 2019 and has suffered a string of injuries since, hampering her progress. She sits 31st in the WTA rankings, having been as high as number four in October 2019.
