Pegula, who is the second-highest seed remaining in the field after Iga Swiatek's withdrawal, had no issue dispatching Canada's Katherine Sebov 6-3 6-1 in just 66 minutes.
Gauff, the six seed, followed suit as she raced to a 6-4 6-3 win over Canadian Rebecca Marino in just 73 minutes.
Florida's own Danielle Collins thrilled her hometown crowd with a 7-6 (7-3) 6-2 triumph against Bulgaria's Viktoriya Tomova, and rising 22-year-old talent Clare Liu made it a perfect 4-0 sweep for the USA representatives by defeating Julia Grabher 6-4 6-3.
Last week's Indian Wells Open champion Elena Rybakina was made to work in her 7-5 4-6 6-3 win over Anna Kalinskaya, while an even more gruelling effort was required in Paula Badosa's two-hour-and-52-minute 7-6 (7-2) 4-6 6-2 result against Laura Siegemund.
The top seed to fall on Thursday was eighth seed Daria Kasatkina, as she won the first set before going down 4-6 6-2 6-2 against Elise Mertens.
Liudmila Samsonova, the 12th seed, made light work of Viktorija Golubic in a 6-1 6-1 drubbing, and 22nd seed Jelena Ostapenko prevailed 6-3 6-4 against Mirjam Bjorklund.
Ostapenko will next play 13th seed Beatriz Haddad Maia after she won a strange back-and-forth contest 7-6 (7-4) 0-6 6-0 over Tereza Martincova.
World number six Pliskova, already frustrated by second-round exits from the US Open and French Open since tennis returned from lockdown, suffered a 4-6 6-4 6-3 defeat to Russian Veronika Kudermetova, despite leading by a set and a break at one point.
Pliskova also lost to the world number 47 at the Western and Southern Open in August, and this was another blow to add to the list of frustrating results for the Czech in the past two months.
Qualifier Gauff succumbed 1-6 7-5 7-6 (7-2) in her clash with Belarusian Aryna Sabalenka, despite having led by a double break at 5-2 in the deciding set.
The American 16-year-old believes she can use the setback as part of her tennis education, saying she needed to play a "smarter" game.
"I just need to play a little bit smarter on pressure points, to make my opponent play," Gauff said, quoted on the WTA website.
"I feel like I wasn't nervous today - I think I just need to be smarter. Sometimes I have tendencies, when it gets to the end, to rush out of the points when instead I should just put the ball in the court."
Belgian Elise Mertens eased to a 6-4 6-2 win over Czech player Karolina Muchova, while Ons Jabeur beat Jelena Ostapenko 6-4 6-4 and US Open semi-finalist Jennifer Brady came from 5-2 behind in the first set to earn a 7-5 6-2 victory over Russian Daria Kasatkina.
Raducanu had to come from a set down to beat Linda Fruhvirtova 4-6 6-4 6-2, while top seed Gauff had an easier time of it as she dismissed Tatjana Maria 6-4 6-1 on another day interrupted by the rain.
Second seed Sloane Stephens was only able to get through three games before play was suspended in her match against Rebeka Masarova, while fifth seed Wang Xiyu was 5-3 down in the first set against Karolina Muchova when the rain came.
Fourth seed Bernarda Pera is out after her match with Viktoria Kuzmova resumed having being washed out on Monday, and the American was unable to prevent a 6-4 6-4 defeat, with Kuzmova advancing to face Raducanu in the last 16.
The only two other matches completed on Tuesday saw Elena-Gabriela Ruse beat Erin Routliffe in three sets, and Anna Blinkova overcome Elisabetta Cocciaretto, also in three.
At the Adelaide International, Zheng Qinwen earned a hard-fought victory against number six seed Anett Kontaveit, eventually winning 6-1 4-6 7-6 (9-7).
Eighth seed Ekaterina Alexandrova also crashed out despite winning the first set against Marketa Vondrousova, going on to lose 4-6 6-3 6-2, though seventh seed Jelena Ostapenko is through after beating Karolina Pliskova 6-1 6-3.
In a contest that lasted over two-and-a-half hours despite only two sets being played, Victoria Azarenka beat Anhelina Kalinina 7-6 (11-9) 7-6 (7-5), and will face Zheng next, while Sorana Cirstea will go up against top seed Ons Jabeur in the last 16 after beating Viktorija Golubic in straight sets.
Raducanu required just 77 minutes to see off the third seed for a 6-2 6-2 win, dominating from the outset to clinch her first final four spot in any tournament since last year's famous US Open triumph.
Having wrapped up the opener with a fierce backhand winner, Raducanu was forced to endure a brief revival from Linette in the second set, before the Pole was troubled by a thigh injury.
Linette lost 14 of the first 17 points on resumption after a medical time out, struggling with her movement as Raducanu saw out the match.
Raducanu has yet to drop a set during her run in Seoul, but will face a stern test in the semi-finals after Ostapenko overcame 17-year-old Victoria Jimenez Kasintseva 6-2 6-1, setting up a first career meeting between the duo.
On the other side of the draw, Ekaterina Alexandrova earned a hard-fought 7-5 7-6 (8-6) win over Lulu Radovcic, but fourth seed Zhu Lin crashed out to Tatjana Maria, losing 6-1 6-1.
In the Pan Pacific Open in Tokyo, meanwhile, Garbine Muguruza fell to a shock 6-4 6-2 quarter-final defeat to Liudmila Samsonova, handing the Russian her 16th win in her last 17 outings.
She will meet Zhang Shuai in the next round, after she became the first Chinese player to make the last four in Tokyo since 2009 by beating Petra Martic 7-5 6-2.
In a battle between the competition's fourth and fifth seeds, meanwhile, Veronika Kudermetova rallied to beat Brazil's Beatriz Haddad Maia 6-7 (4-7) 7-6 (8-6) 6-1.
The world number 12 was trailing 6-2 2-1 when calling time on the match against Andreescu in a highly anticipated showdown between two of the past three US Open winners.
Raducanu initially left the court for treatment ahead of the seventh game of the opening set for a medical timeout and completed just four more games.
Speaking after her withdrawal, coming two weeks before the French Open, Raducanu explained she did not want to aggravate an injury sustained at last week's Madrid Open.
"I thought maybe taking one, two days off, it would go away because a lot of the other small niggles I've had, they've kind of gone away after taking, like, two days off," she said.
"Then I got here and I was training, but it just didn't seem to get better. I was training with some limitations. I wasn't moving really.
"I was just playing where I knew where the ball was coming, just staying in one corner. I think I must have underestimated the unpredictability of competition in a match.
"The last few weeks have been really positive. I've learned a lot about myself and my game has definitely improved on this surface but I need to make sure my back is fully right.
"I need to just keep on it. I don't want to play my next match with a feeling of limitation because I think that I learned my lesson from this week, when to push, when not to push."
Ons Jabeur joined Andreescu in the last 32 with a 6-0 7-6 (7-1) victory over Sorana Cirstea to keep her impressive run of form going.
The Tunisian won her first WTA 1000 title in Madrid last week and has now won seven successive main draw matches for the first time in her career
Elsewhere in Tuesday's action, American qualifier Lauren Davis pulled off a shock 6-2 6-3 win against number 11 seed Jelena Ostapenko.
Fellow Americans Jessica Pegula, Madison Brengle and Amanda Anisimova also advanced, beating Liudmila Samsonova, Marta Kostyuk and Tereza Martincova respectively.
Anisimova, who is now the player with the most wins in three sets so far in 2022 with nine, will face Belinda Bencic for a place in the last 16.
The 2021 US Open winner was featuring in her first semi-final since that fairytale triumph at Flushing Meadows, and took the opening set 6-4 after making a flying start on Saturday.
Ostapenko then fought back to level the match, with Raducanu first appearing to struggle with her movement when she was a break up in the second, forcing her to take an off-court medical timeout.
The 19-year old later retired citing a left glute injury when 3-0 down in the decider, ending her confidence-boosting run in Seoul and teeing up a final meeting between the top two seeds.
Indeed, Alexandrova enjoyed a more routine outing in her meeting with Wimbledon semi-finalist Tatjana Maria, downing the German 6-2 6-4 to advance to her second final of the year.
At the Pan Pacific Open in Tokyo, meanwhile, Chinese teenager Zheng Qinwen reached her first WTA Tour final with a hard-fought win over world number 13 Veronika Kudermetova.
Having required over three hours to seal her 5-7 6-3 7-6 (7-3) triumph, the world number 36 said: "After the match when I won the last point, the feeling was incredible.
"The opponent, she's playing unbelievable tennis. She has a really good serve and hits the ball hard, she moves well. It's my first time in the final. I'm so happy."
Her compatriot Zhang Shuai was unable to replicate those exploits, however, as Liudmila Samsonova eased into her third WTA final of the year with a 7-6 (7-4) 6-2 win.
In-form Samsonova has won both of her previous final appearances this year - each of which came last month - and is 3-0 in showpiece matches for her career.
The 22-year-old Pole had not dropped a set on her way to the fourth round, but she had never beaten Ostapenko in three previous career meetings.
Swiatek took the first set with relative ease but then Ostapenko’s sledgehammer of a forehand started finding its mark to level the match.
A one-sided final set saw former French Open champion Ostapenko triumph 3-6 6-3 6-1.
Swiatek’s defeat means that Aryna Sabalenka of Belarus will take over as world number one after the tournament.
Ostapenko will face Coco Gauff in the quarter-finals after the teenager ended the grand slam comeback of mother-of-two Caroline Wozniacki.
The 19-year-old came from a break down in the first and third sets to win both and complete a 6-3 3-6 6-1 victory.
Wozniacki’s return has been one of the stories of New York this year, having come out of retirement after more than three years and two children later.
The 33-year-old former world number one has looked as though she has never been away, but a fired-up Gauff proved just too strong in the deciding set.
Wozniacki got off to a dream start with a break in the first game and a 2-0 lead.
But Gauff quickly got back on the board, levelling at 3-3 before going on to clinch the first set without dropping another game.
Wozniacki cranked up the pressure in the second and Gauff started feeling it as her suspect forehand began to misfire and she was broken for 5-3 as the Dane levelled the match.
Gauff looked uncomfortable as she dropped serve again at the start of the decider, but after pointedly ignoring the advice of coach Brad Gilbert, the wound-up American began firing backhand winners as if they were going out of fashion.
She reeled off the next six games to clinch the victory and let out a loud scream of triumph after converting match point.
“Definitely getting it to 2-1 (in the third set) was the turning point,” said Gauff.
“I got broke and I showed I was still in the match. I started to go for my shots.
“Caroline, it’s like she’s never left, the level she played was amazing. It’s weird because I grew up watching Caroline and when she won the Australian Open, so to be on court with her today was an honour.
“She definitely gets to a lot of balls. I felt a bit like I was playing myself. I knew I had to play aggressive and go for my shots. In some moments I miss but I was happy I could get back and refocus.”
It will be the fifth grand slam quarter-final of Gauff’s still-fledgling career and her second at Flushing Meadows.
“I’ve been in this position before,” she added. “And I think I have confidence in myself that I can go even further.”
Playing for the first time since she was knocked out of the Australian Open by Elena Rybakina in the fourth round last month, normal service was resumed by the domineering world number one in Doha.
The top seed brushed Collins aside in only 53 minutes, racing to a 6-0 6-1 victory to march into the third round.
Collins only won four points as she suffered the misery of a first-set bagel, an inspired Swiatek taking the opener in only 21 minutes.
Swiatek's run of games won was ended at nine when Collins got on the board at 3-1, but the Pole broke for a fifth time before serving it out for an emphatic victory.
The 21-year-old three-time grand slam champion, who made only six unforced errors, will do battle with Belinda Bencic for a place in the quarter-finals.
Bencic beat two-time champion Victoria Azarenka 1-6 7-6 (7-4) 6-4 to take her place in the last 16, storming back from 4-1 down in the second set when she appeared to be on her way out.
Second seed Jessica Pegula saved two match puts as she dug deep to beat Jelena Ostapenko 6-2 2-6 7-5 to set up a meeting with Beatriz Haddad Maia, who beat Daria Kasatkina in straight sets.
Fourth seed Coco Gauff got the better of Petra Kvitova 6-3 7-6 (8-6), while Veronika Kudermetova and Maria Sakkari also made it through.
Kazakhstan's Rybakina, who is also the reigning Wimbledon Champion and Australian Open finalist, got the better of Badosa for the second time during her current run, also eliminating her from Indian Wells.
The 23-year-old has to be considered one of the favourites to go all the way, having knocked off world number one Iga Swiatek and world number two Aryna Sabalenka to lift the trophy in California.
Rybakina will meet Belgium's Elise Mertens in the fourth round after she beat Croatia's Petra Martic 6-4 6-3.
Meanwhile, the biggest upset of the day was delivered by Russia's Anastasia Potapova, bouncing sixth seed Coco Gauff 6-7 (8-10) 7-5 6-2.
Potapova, who has never won a tournament above the WTA 250 level, will face China's Zheng Qinwen for a spot in the quarter-finals after her three-hour 5-7 7-6 (7-5) 6-3 triumph over Liudmila Samsonova.
Latvia's Jelena Ostapenko, the 24th seed, eliminated Brazilian 13th seed Beatriz Haddad Maia 6-2 4-6 6-3, while 20th seed Magda Linette of Poland knocked out Belarusian 14th seed Victoria Azarenka 7-6 (7-3) 2-6 6-4.
Unseeded American Clare Liu went down 4-6 7-5 6-4 against Italy's Martina Trevisan, but third seed Jessica Pegula will continue to fly the flag for the United States after advancing 6-1 7-6 (7-0) in her all-American showdown with Danielle Collins.
It was an ominous start for Cirstea, being broken to love in the opening game, but she stuck with second seed Sabalenka and broke back, before ultimately being pipped to the first set by the impressive Belarusian.
The key was on break points, with Sabalenka claiming all five that she won against the Cirstea serve, while saving six of eight on her own as she ultimately eased to victory.
Sabalenka now has 26 wins on clay in the WTA since 2021, with only Ons Jabeur (37), Iga Swiatek (34), Paula Badosa (31) and Coco Gauff (28) having more during this time.
Gauff also advanced after a routine 6-4 6-1 win over Irene Burillo Escorihuela, making the sixth seed in Madrid the first player to win 35 WTA-1000 main draw matches as a teenager since 2009.
Ninth seed Maria Sakkari defeated Arantxa Rus 6-4 6-4 and fifth seed Caroline Garcia also had few problems against Yulia Putintseva, winning 6-3 6-4.
However, it was not a good day for 10th seed Petra Kvitova, who was beaten 7-6 (11-9) 6-1 by Jule Niemeier, while 13th seed Beatriz Haddad Maia also lost, 7-6 (8-6) 6-3 to Mirra Andreeva and 20th seed Donna Vekic was eliminated in straight-sets by Rebeka Masarova.
Jelena Ostapenko took just 61 minutes to get past Linda Fruhvirtova 6-0 6-3, and will face 14th seed Liudmila Samsonova next, who did not take much longer to see off Maryna Zanevska 6-2 6-3.
There were also wins for Elise Mertens, Badosa, Camila Osorio, Shelby Rogers, Mayar Sherif, Magda Linette and Irina-Camelia Begu.
The Belarusian, who recovered from a lower back injury sustained in her previous match against Elina Svitolina, breezed through 6-2, 6-4 after just 72 minutes on the court.
Sabalenka broke her serve in the third and fifth games, with Ostapenko opening the door with two double faults, while a single break in the seventh game settled the second set.
The second seed almost let it slip with her only double fault but came back with two big serves to close out the win.
Sabalenka will face Danielle Collins or Victoria Azarenka in the semi-final on Friday.
Data Debrief: Top 10
Sabalenka (10) has become only the second player to reach 10 or more WTA-1000 semi-finals since the start of the 2020 season, along with Iga Swiatek (16).
With Sabalenka joining Swiatek and Coco Gauff, it is the first time the WTA’s top three players have reached the semi-final at the same WTA event since Roland Garros in 2013 – excluding the WTA Tour Finals.
Sabalenka has spent the most time out on the court in WTA clay events in 2024, with this match bringing her up to 25 hours and 34 minutes.
Belarus' Sabalenka needed just 66 minutes to defeat the Russian 6-2 6-0, taking advantage of her first-round bye to book her spot in the third round against Ukraine's Lesia Tsurenko.
Tsurenko had to come from behind against the in-form Donna Vekic, fresh off her Monterrey Open title last week, but that big effort may have had the Croatian with heavy legs as she ran out of steam 2-6 6-2 6-2.
It was a strong day for the Ukranians as 27th seed Anhelina Kalinina beat the Czech Republic's Linda Fruhvirtova 4-6 6-4 7-5, and she will next face Greece's Maria Sakkari.
Sakkari, the seventh seed, had to deal with adversity after a poor first set against Shelby Rogers, coming back to win 2-6 6-4 6-0.
Olympic gold medallist Belinda Bencic lost her Swiss showdown against Jil Teichmann 3-6 6-3 6-3, while Veronika Kudermetova got the better of her Russian compatriot Anna Blinkova 6-3 6-4.
The second-highest ranked American in the field, Coco Gauff, had no issues dispatching Spain's Cristina Bucsa 6-2 6-4. But it was tougher work for America's top hope Jessica Pegula as she was pushed all the way by recent Merida Open champion Camila Giorgi, before prevailing 3-6 6-1 6-2.
Sakkari beat world number five Svitolina 6-3 6-3 to progress to the last eight of a WTA Premier event for the third time this season.
Unseeded Greek Sakkari struck 32 winners and returned superbly, winning all but eight of 29 points on Svitolina's second serve.
The 23rd-ranked Sakkari will face either wildcard Jelana Ostapenko or Ons Jabeur for a place in the semi-finals.
Ostapenko knocked out fifth seed Petra Martic, the 2017 French Open champion easing to a 6-3 6-1 victory.
Martic had won their previous two meetings, but the Croatian was beaten in just 57 minutes at the indoor hard-court event.
Anett Kontaveit was another seed to fall, Sara Sorribes Tormo reaching a maiden Premier-level quarter-final at the expense of the Estonian with a 6-1 6-4 success.
Victoria Azarenka is also two wins away from the final, coming from a set down to see off Barbora Krejcikova 2-6 6-2 6-1, and will now face Karolina Muchova or Elise Mertens, who got past Amanda Anisimova in straight sets.
Top seed Sakkari beat Anastasia Potapova 6-4 6-4 to advance to the last 16, while seventh seed Ostapenko was a 6-1 6-4 winner against wildcard Wang Xinyu.
Kvitova, the 2018 champion, took just an hour and nine minutes to see off qualifier Jule Niemeier 6-2 6-1, with the sixth seed and two-time former Wimbledon winner making a positive first appearance since being eliminated from the Australian Open in round one.
Sakkari, Ostapenko and Kvitova followed fellow seeds Anett Kontaveit, Belinda Bencic and Elise Mertens - winners on Monday - in avoiding an early exit.
However, number four seed and home favourite Anastasia Pavlyuchenkova was forced to withdraw from the competition on Tuesday due to a knee problem.
Bernarda Pera replaced the Russian in the main draw and fell 7-6 (7-3) 6-4 to Jaqueline Cristian, who will next face Aliaksandra Sasnovich.
That is after Sasnovich held firm to beat Magda Linette 7-5 4-6 6-4 in a tight contest, with a decisive break in the fifth game of the third set seeing her through.
Williams and Halep played in an exhibition event with a crowd of 4,000 watching on in Adelaide last Friday and they were back in competitive action three days later.
Legendary American Williams beat Daria Gavrilova 6-1 6-4 to move into the third round of the Yarra Valley Classic.
The fifth seed struck 27 winners to 15 unforced errors on Margaret Court Arena as she set up a meeting with Tsvetana Pironkova, who ousted Donna Vekic 1-6 6-4 6-2.
Williams said: "It was a good match for me. It wasn't easy at all. It was lots of rallies and lots of movement, and she's from here, so she obviously always plays hard. So it was really good and it felt good to clinch that in the end."
Third seed Karolina Pliskova, Petra Martic, Danielle Collins and Marketa Vondrousova also advanced to the last 16 on Monday.
Elsewhere, top seed Halep is through to the third round of the Gippsland Trophy following a 6-4 6-4 win over Anastasia Potapova.
Halep hit 23 winners and broke twice in each set in what was her first official match since October.
Elina Svitolina, the third seed, beat Andrea Petkovic 6-1 6-4, while Coco Gauff, Ekaterina Alexandrova and Jelena Ostapenko were among the other winners seven days prior to the start of the first grand slam of 2021.
In doing so, Williams became the fourth player since 2000 to win a WTA-level main draw match after turning 40, joining sister Venus Williams, as well as Kimiko Date Krumm and Martina Navratilova.
She also claimed the all-time record for wins at the Canadian Open, with 35, now one more than Chris Evert.
"I guess there’s just a light at the end of the tunnel," Williams said after the match. "I don’t know, I’m getting closer to the light. Lately that's been it for me. I can’t wait to get to that light."
She added: "I love playing though, so it’s like amazing. But I can’t do this forever. Sometimes you just want to try your best to enjoy the moments and do the best that you can."
Williams' older sister Venus, 42, was beaten on Monday by Swiss Jil Teichmann 6-2 6-3 with the match finshing after midnight following a delayed start due to rain.
One of the three seeded players in action on Monday, 15th seed Simona Halep had no issues cruising through the challenge of Donna Vekic 6-0 6-2.
It was similarly smooth sailing for 14th seed Karolina Pliskova in her all-Czech showdown against Barbora Krejcikova, winning 6-3 6-4, while Latvian 16th seed Jelena Ostapenko handled the challenge of Ukraine's Anhelina Kalinina 6-4 6-2.
Kazakhstan's Elena Rybakina defeated in-form qualifier Marie Bouzkova 7-5 6-7 (3-7) 6-1, likely earning a shot at Coco Gauff if the American wins as a heavy favourite tomorrow, while Brazil's Beatriz Haddad Maia beat Italy's Martina Trevisan 6-2 2-6 6-2 in a meeting of two top-30 players.
In a pair of all-American battles, Sloane Stephens edged Sofia Kenin 6-2 7-6 (7-5) 7-5, and world number 187 Asia Muhammad upset world number 25 Madison Keys in straight sets 7-6 (7-5) 6-4.
Alize Cornet defeated her French compatriot Caroline Garcia 3-6 6-3 6-3, and Canada's Katherine Sebov was unable to get the job done in front of her home fans, going down 6-3 2-6 5-7 to Yulia Putintseva.
In better news for the Canadians, Leylah Fernandez won 6-4 6-7 (2-7) 6-3 over Storm Sanders, while veteran two-time Wimbledon winner Petra Kvitova was beaten by Alison Riske 6-2 4-6 6-3.
The world number five lost 6-4 7-6 (7-3) to 21st-ranked Rybakina, whose reward is a meeting with Coco Gauff's conqueror Anastasija Sevastova in the quarter-finals.
Third seed Bianca Andreescu of Canada also lost in straight sets, Anett Kontaveit of Estonia beating her 6-3 6-3.
And it was the same story for fourth seed Iga Swiatek, though she at least took a set as she was beaten by Daria Kasatkina.
It took an impressive rally from Russia's Kasatkina to bounce back from losing the first en route to a 4-6 6-0 6-1 success.
She will now face Jelena Ostapenko, who beat Ons Jabeur 5-7 6-4 6-3.
In fact, top seed Aryna Sabalenka was the only seed to avoid a surprise exit on Wednesday as she cruised through.
The Belarussian, ranked fourth in the world, beat Alison Riske 6-1 6-4 in just over an hour to set up a clash with Camila Giorgi.
Giorgi had earlier followed up a win over defending champion Karolina Pliskova in the last round by beating Shelby Rogers 6-3 4-6 6-2.
There was no such string of shocks at Wednesday's other WTA event, the Bad Homburg Open in Germany, though first and second seeds Petra Kvitova and Victoria Azarenka needed three sets to progress.
Kvitova lost a second-set tie-break as she beat Ann Li 6-2 6-7 (4-7) 6-1 to reach the quarters, while Azarenka defeated Alize Cornet 6-4 3-6 7-6 (9-7).
Angelique Kerber, the fourth seed, progressed more smoothly, earning a comfortable 6-0 6-2 win over Russia's Anna Blinkova.
And Nadia Podoroska saw off the challenge of Patricia Maria Tig, winning 7-6 (7-4) 2-6 6-4.
Svitolina – the fourth seed – dropped the first set to 32nd seed Sorana Cirstea before fighting back to reach the round of 16 at the WTA Premier 1000 event on Sunday.
Two-time grand-slam champion Azarenka joined Svitolina in the next round after knocking out seventh seed Petra Kvitova, but 11th seed Halep became Aliaksandra Sasnovich's latest conquest.
SVITOLINA SURVIVES CIRSTEA SCARE
Svitolina needed two hours, 32 minutes to outlast Cirstea 4-6 6-4 7-6 (7-3) and remain unbeaten in three career matches against the Romanian.
The Ukrainian was on the defensive throughout the opening set, facing 11 break points on her serve and managing to save eight of them before Cirstea finally won out.
Svitolina tightened things up from there, saving four of five break points the rest of the match.
"It was a very tough match today, and I was fighting and trying to find my game," said Svitolina, who will face Jessica Pegula next. "It was a bit of a rollercoaster.
"I wish I could play a little bit better in the first set, I had chances to grab that set, but unfortunately it didn't play the way I wanted. I had to fight for every point, and Sorana played a great match, I think. I'm happy that I could win today."
AZARENKA TAKES DOWN KVITOVA
Azarenka won her first two Tour-level matches against Kvitova in 2008 and 2009 but had prevailed only once in six meetings since then before Sunday's 7-5 6-4 triumph.
The two-time Indian Wells champion converted break-point chances when she needed them, six of 11 in all, and had 18 unforced errors to Kvitova's 26.
"It was important to just stay there, really take my opportunities, not to let her," Azarenka said after taking down two-time Wimbledon winner Kvitova. "If she gets in the groove in couple points, not to kind of let her extend that streak, if you want to call it that.
"I was trying to still create opportunities for myself, be more aggressive, and honestly just believing also that what I'm doing is right and see how I can execute that. So intention was good. Execution followed after."
ANOTHER UPSET FOR SASNOVICH
After knocking off US Open champion Emma Raducanu in the second round, Sasnovich ushered out another grand slam winner in Halep 7-5 6-4 and will next face Azarenka.
The world number 100 had 22 winners to 16 for Halep and won 61.8 per cent of points on her serve as she reached the round of 16 at Indian Wells for the first time.
In other matches Sunday, ninth seed Anastasia Pavlyuchenkova fell to 23rd seed and US Open runner-up Leylah Fernandez 5-7 6-3 6-4, while second seed Iga Swiatek dropped only one game in a 6-1 6-0 demolition of Veronika Kudermetova.
Jelena Ostapenko and Shelby Rogers also advanced.
The world number one cruised to a 6-1 6-1 triumph over 2021 US Open finalist Leylah Fernandez, just three days after winning the Qatar Ladies Open in Doha.
That marked Swiatek's 41st main-draw victory in WTA 1000 events in just her 53rd outing, only Serena Williams and Maria Sharapova (52 each) have won more than 40 such matches in fewer attempts.
The 21-year-old has won her last 35 hard-court matches against opponents ranked outside the world's top 30, though Swiatek said she had to adapt against Canada's Fernandez.
"It wasn't that easy for sure. It was much tougher than the score said," said Swiatek, who will look to make the fourth round for the first time in Dubai when she faces Liudmila Samsonova.
"In the second set... I needed to go a level up. I didn't have much time to get used to the conditions, but I'm just happy I could play solid tennis."
Jessica Pegula, the third favourite at the tournament, defeated Viktoriya Tomova 6-2 5-7 6-1 to set up a third-round battle with Ana Bogdan, who overcame Shelby Rogers 7-6 (7-3) 6-3.
Fifth seed Coco Gauff coasted past Aliaksandra Sasnovich with a 6-0 6-4 victory, teeing up a meeting with Elena Rybakina, who slammed six aces in a 7-5 6-2 defeat of Marie Bouzkova.
World number two Aryna Sabalenka, who defeated Rybakina at this year's Australian Open final, made light work of lucky loser Lauren Davis in a straight-sets rout as she claimed her 12th straight win in 2023.
Dubai's defending champion Jelena Ostapenko will be the next challenge for Sabalenka after defeating 17-year-old Linda Fruhvirtova for her seventh straight win at the event.
Barbora Krejcikova saved four match points en route to a 6-4 4-6 7-5 win over seventh seed Daria Kasatkina and will meet Karolina Pliskova next after she downed sixth favourite Maria Sakkari in straight sets.
Belinda Bencic and Marta Kostyuk played out the match of the day as the former claimed a 6-7 (7-9) 7-6 (7-5) 6-4 triumph, with that clash taking three hours and 27 minutes – the second-longest on the WTA Tour this year.
Swiatek was swept aside by Jelena Ostapenko in the battle between two previous French Open champions in the desert.
Elina Svitolina, reigning Roland Garros champion Barbora Krejcikova and US Open runner-up Leylah Fernandez were also sent packing from the WTA Premier 1000 event.
SWIATEK CRUMBLES
After top seed Karolina Pliskova was eliminated on Monday, 2020 French Open champion Swiatek crashed out following a 6-4 6-3 defeat to Ostapenko.
Ostapenko – the 2017 Roland Garros winner – rallied from a break down in each set to reach the quarter-finals at Indian Wells, where the 24th seed hit 25 winners to 21 unforced errors in 93 minutes.
"I knew it was going to be a very tough match because she's such a great player, she won a grand slam and she's playing great tennis," Ostapenko said.
Standing in the way of Ostapenko and the semi-finals is Shelby Rodgers, who edged Flushing Meadows finalist Fernandez 2-6 6-1 7-6 (7-4).
SVITOLINA UPSTAGED BY PEGULA
Svitolina's campaign in the desert did not go according to plan, the fourth seed crushed 6-1 6-1 by Jessica Pegula.
Pegula – the 2021 Australian Open quarter-finalist – dismantled Svitolina in just 68 minutes for her seventh last-eight appearance of the season and fourth at WTA 1000 level.
"I think I've just been making a lot of really good decisions in the right moments," said Pegula, who will face two-time grand slam champion Victoria Azarenka following her seventh top-10 victory. "That obviously comes with playing a lot of matches, winning and getting confidence... it's just been more belief that I can play at this level. I think this year, I realised that, and I've been having good results."
KERBER POWERS THROUGH AS KREJCIKOVA FALLS
Three-time major winner and 10th seed Kerber will feature in the quarter-finals after overpowering Ajla Tomljanovic 6-4 6-1.
Kerber will next meet 21st seed Paula Badosa, who shocked third seed and reigning French Open champion Krejcikova 6-1 7-5.
"I think I played a pretty good match today," Badosa said. "I knew I had to play on a high level against Barbora. She's an amazing player, very talented. We played before so I knew what I was going to find there on court. I'm feeling good and I'm very happy that I could play my best today."
