Stephens, who is currently ranked 73rd in the world, having been number three on the WTA Tour in 2018, triumphed 6-7 (5-7) 7-5 6-1 over Watson in two hours, 50 minutes on Wednesday.
In a see-sawing match, there were six breaks in the opening set, as Watson got the edge early on Stephens' serve at the WTA Premier 1000 event.
Stephens steadied by claiming a late break in the second to level the match, before dominating the third set.
Playing at her 10th Indian Wells Open, Stephens won seven consecutive games after the match was 5-5 in the second set.
"After the first set, that was disappointing to lose that one, but I felt like it was a battle and I was still in the match," Stephens said. "I knew I had to keep fighting and that's what I did, and I'm just really pleased to have squeaked out a win here."
KEYS ON SONG IN OPENER
Former world number seven Madison Keys moved through to the second round with a 6-0 7-5 win over fast-finishing Estonian veteran Kaia Kanepi.
American Keys won 21 consecutive points as part of a streak where she clinched the first nine games of the match, withstanding Kenapi's late push.
Keys will take on Russian ninth seed Anastasia Pavlyuchenkova for a spot in the third round.
SAMSONOVA, MARTIC, ROGERS AND PUTINTSEVA PROGRESS
Liudmila Samsonova, who made the fourth round at Wimbledon earlier this year, needed more than two hours to get past Ukrainian qualifier Kateryna Kozlova 6-4 7-6 (8-6).
Samsonova will face countrywoman and 25th seed Veronika Kudermetova in the second round.
Petra Martic won through to take on second seed Iga Swiatek with a 6-4 6-4 victory over American wildcard Katie Volynets.
Ash Barty's US Open conqueror Shelby Rogers claimed her 25th win for the year, getting past Ukrainian Anhelina Kalinina 7-6 (7-2) 6-2, while Yulia Putintseva won 7-6 (7-2) 6-1 over experienced German Andrea Petkovic to set up a showdown with fellow Kazakh player and 13th seed Elena Rybakina.
The Ukrainian defeated Ana Bogdan 7-5 6-2 on Saturday to reach the last 16 for the sixth time in her career.
Both players struggled on serve, with 11 breaks in total during the match, but it was Svitolina who ultimately emerged triumphant after a back-and-forth contest and a rain delay, firing 28 winners.
Fifteenth seed Svitolina will now hope to halt the Paris charge of fourth seed Rybakina, who is yet to drop a set at the tournament so far. It will be a tough ask, but Svitolina does lead the head-to-head 2-1.
An all-American clash between Madison Keys and Emma Navarro on Court Suzanne-Lenglen was one of the other standout matches.
Navarro had never before reached the fourth round at a major, while Keys was a former semi-finalist at Roland-Garros.
But it was Navarro who claimed a hard-fought victory, getting the better of two tie-breaks to win 7-6 (7-5) 7-6 (7-3) to book a huge clash against second seed Aryna Sabalenka.
Jasmine Paolini is also through to round four after seeing off former US Open champion Bianca Andreescu 6-1 3-6 6-0.
Mirra Andreeva, meanwhile, is the youngest player to reach the French Open last 16 since Nicole Vaidisova in 2006 after beating Peyton Stearns in straight sets.
The 17-year-old raced to a 6-2 6-1 win in only 67 minutes.
Sabalenka and Rybakina had earlier completed routine victories over Paula Badosa and Elise Mertens respectively.
The top seed, who made it to the final last year, dropped a set for the first time in this tournament before recovering to win 4-6 6-0 6-2 in a match that lasted just short of two-and-a-half hours.
These two players met in the French Open semi-finals last year and 11th seed Haddad Maia was eyeing an upset when she fought back from 4-1 down to claim the opener.
But Swiatek dropped serve just once in the next two sets as she assumed full control and swept to victory, powered by winning eight straight games from the start of the second set.
Data Debrief: Swiatek statistics up there with the best
Up next for Swiatek will be a last-four clash against either Ons Jabeur or Madison Keys, who play later on Tuesday. That will be her 15th WTA 1000 semi-final appearance since 2020, with no other player having made it to double figures (Aryna Sabalenka and Maria Sakkari are the next best on eight each).
Beating Haddad Maia also means Swiatek has equalled Serena Williams and Maria Sharapova as the fastest player to reach 25 WTA 1000 wins on clay, doing so in just 29 matches.
And Swiatek's emphatic second set saw her tie Coco Gauff for the most number of 6-0 sets won so far this year. They both have seven, just ahead of Sabalenka (five).
Defending champion Sabalenka plays Mirra Andreeva in the last eight on Wednesday after battling past Danielle Collins in three sets. All three of her wins so far have been in deciding sets.
The other last-eight clash is between Elena Rybakina and Yulia Putintseva.
Swiatek was irrepressible against the 18-year-old American, extending her head-to-head dominance to 4-0 with a 6-0 6-3 victory in 66 minutes.
The Pole won the first eight games of the match and always appeared in control with her reliable forehand a key feature.
Swiatek laced 13 winners with only nine unforced errors, breaking Gauff five times. The American committed 26 unforced errors for the match.
The victory is Swiatek's 62nd of the season, moving her closer to Angelique Kerber's 2016 mark of 63.
Swiatek will face fourth seed Jessica Pegula in the semi-finals as the Pole aims for her eighth WTA title of the season.
Pegula secured her berth in the final four with a 6-4 7-5 victory over compatriot Madison Keys in their first-ever meeting in one hour and 34 minutes.
Third seed Aryna Sabalenka was a surprise casualty as Croatian qualifier Donna Vekic continued her excellent week with a 6-4 6-7 (5-7) 6-1 in two hours and 37 minutes.
World number 77 Vekic has beaten former world number three Maria Sakkari and two-time major finalist Karolina Pliskova this week.
Second seed Paula Badosa was also bundled out by American Danielle Collins 7-6 (7-5) 6-4. Collins will meet Vekic in the last four.
The 2022 French Open and US Open champion triumphed 6-4 4-6 6-1 in two hours and two minutes, bouncing back strongly after losing the second set.
Zheng's power and forehand top spin proved challenging for the Pole, who was solid from the baseline to secure her 11st tour quarter-finals appearance this season.
The Chinese had broken Swiatek to lead 1-0 in the third set, but the top seed responded in trademark style, improving her record in the United States this season to 21-1.
Swiatek will take on eighth seed Coco Gauff in the quarter-finals, with the match-up marking a re-match of this year's French Open final.
Gauff worked her way into the last eight with a 6-4 4-6 6-3 victory over 2019 US Open champion Bianca Andreescu.
The 18-year-old American also had to fight back from a set down in the third set to win in a match that lasted just over two-and-a-half hours.
Third seed Aryna Sabalenka fought back from a lopsided opening set to knock out American Sloane Stephens 1-6 6-3 6-2 in two hours and one minute. The Belarussian will take on Donna Vekic in the next round.
Second seed Paula Badosa eased into the last eight, winning in 53 minutes against American qualifier Louisa Chirico 6-0 6-3. Badosa will face Danielle Collins in the quarter-finals.
Madison Keys triumphed over eighth seed Daria Kasatkina 6-4 6-3 in one hour and 27 minutes to secure a quarter-final date with fourth seed Jessica Pegula.
Swiatek had been forced to fight back from a set down against Beatriz Haddad Maia in the quarter-finals, but there was no slow start on Thursday as she broke Keys' serve to love at the first attempt.
Only in the fifth game, when Keys failed to convert two break points, was Swiatek troubled in a 31-minute opener, and she carried that momentum into the second set with another early break.
Having eliminated Coco Gauff and Ons Jabeur on a deeply impressive run, Keys had no answer for Swiatek's power as she clinically worked her way through the second set, the American's forehand running long on match point to seal a routine win for the world number one.
Having lost last year's final against Aryna Sabalenka, Swiatek could face a rematch against the defending champion, who takes on Elena Rybakina in Thursday's other semi-final.
Data Debrief: Swiatek surpasses Serena
Saturday's final will be Swiatek's 11th at WTA 1000-level, the Pole going all the way on 37.9 per cent of her 29 main-draw entries at that level. That is a better ratio than 23-time grand slam champion Serena Williams managed in her glittering career, the American doing so at 18 of 49 WTA 1000 tournaments (36.7 per cent).
Swiatek has now played eight matches in 2024 without dropping a single game on her own serve, a tally only matched by her possible final opponent Sabalenka on the WTA tour.
Poland trailed after Lorenzo Musetti and Matteo Berrettini secured wins against Daniel Michalski and Hubert Hurkacz respectively, only for Swiatek and Magda Linette to level things with respective singles victories over Martina Trevisan and Lucia Bronzetti.
That sent the Brisbane city final to a decider in the mixed doubles, which Swiatek and Hurkacz won with ease 6-1 6-2 against Musetti and Camilla Rosatello, though there was a pause in the second set to dry rainfall on the court.
Despite defeat, Italy also advanced to the final four as the city finals loser with the best record.
It was more routine in Sydney as the United States eased to a 4-1 win against Great Britain.
Madison Keys came from a set down to beat Katie Swan, while Jessica Pegula eased past Harriet Dart 6-2 6-0 after Cameron Norrie had defeated Taylor Fritz in three sets.
Despite going a set behind, Frances Tiafoe came back to beat Dan Evans 3-6 7-5 6-3 to clinch the win for his country, before Pegula and Fritz added some gloss after beating Dart and Evans in the mixed doubles.
The third city final in Perth included a thriller as Greece's Stefanos Tsitsipas beat Borna Coric 6-0 6-7 (4-7) 7-5. Donna Vekic had no trouble getting Croatia on the board as she eased past Despina Papamichail 6-2 6-0.
Maria Sakkari put Greece 2-1 ahead when she beat Petra Martic 6-3 6-3, but Borna Gojo defeated Stefanos Sakellaridis in straight sets to make it 2-2.
However, Greece secured the win and their place in the last four after the pairing of Sakkari and Tsitsipas saw off Martic and Gojo 7-6 (8-6) 6-4.
Greece will take on Italy in the semi-finals, while Poland face the USA, with both taking place in Sydney on Friday.
The world number one took just 76 minutes to wrap up a commanding 6-1 6-3 win - matching the scoreline which saw her overcome the American in the Madrid Open last four a fortnight ago.
Swiatek broke her opponent four times and saved all 10 break points she faced on the way to setting up a semi-final showdown with either Coco Gauff or Qinwen Zheng.
Yet to drop a set this week, the Pole remains on course to complete a hat-trick of titles in Rome and land her fourth silverware of 2024, in which she now boasts a 36-4 record.
Data debrief
Reaching her 16th WTA 1000 semi-final from 30 main draws entered, Swiatek (53.3 per cent) surpasses Serena Williams (53.1 per cent, 26 from 49) for the highest rate of last-four appearances in such tournaments since the format's introduction in 2009.
The Pole also took her tally of WTA match wins on clay to 75 from 85, with only Monica Seles, Nancy Richey (both 80), Chris Evert (81) and Margaret Court (82) reaching that figure on surface in fewer matches during the Open Era.
ATP world number four Tsitsipas is one of the headline names in action at the event, which is acting as a warm-up tournament for the Australian Open.
After going a set down to his Bulgarian opponent in his first game of the inaugural tournament, Tsitsipas hit back with a strong second set before holding his nerve in a tense tie-break in the decider, securing a 4-6 6-2 7-6 (7-4) win.
Tsitsipas's team-mate Despina Papamichail continued Greece's strong start, also coming from a set down to beat Isabella Shinikova 3-6 6-4 6-1.
Great Britain opened with a pair of victories, Cameron Norrie and Katie Swan earning straight sets triumphs over their Australian counterparts in Sydney.
Norrie, who was initially set to play Nick Kyrgios prior to the Wimbledon finalist's withdrawal due to an ankle injury, eased to a 6-3 6-3 victory over Alex De Minaur, while Swan defeated Zoe Hives.
The United States are also taking a 100 per cent record into day two of the tournament, after Taylor Fritz and Madison Keys overcame Jiri Lehecka and Marie Bouzkova respectively, while France pair Arthur Rinderknech and Alize Cornet got off to winning starts against Argentina's Francisco Cerundolo and Maria Lourdes Carle.
In Brisbane, Swiss hope Belinda Bencic secured a 7-6 (7-0) triumph over Yulia Putintseva of Kazakhstan and Beatriz Haddad Maia, the Brazilian world number 15, dispatched Italy's Martina Trevisan 6-2 6-0.
Former world number one and third seed Williams prevailed in a tricky test against Margarita Gasparyan in straight sets in New York on Thursday.
Countrywoman and second seed Kenin contained Canadian teenager Fernandez behind closed doors at Flushing Meadows.
It was not good news for 10th seed Muguruza, who was sent packing by unranked Bulgarian Tsvetana Pironkova.
SERENA WINS THROUGH
Williams continued her quest for a record-equalling 24th grand slam after defeating Russian Gasparyan 6-2 6-4 to set up a showdown with 2017 US Open winner Sloane Stephens.
The 38-year-old Williams hit 27 winners and just 16 unforced errors, an improvement on her numbers in the opening round, under the Arthur Ashe Stadium lights.
Williams, who has not won a slam since the 2017 Australian Open, will next meet Stephens after the American 26th seed eased past Olga Govortsova 6-2 6-2.
KENIN SEES OFF FERNANDEZ
Kenin advanced to the third round of her home slam for the fourth year in a row thanks to a 6-4 6-3 victory over Fernandez.
World number four Kenin did not face a break point in a contest lasting one hour, 21 minutes.
After firing 19 winners and three aces, Kenin will play Ons Jabeur – who took down Kaia Kanepi 7-6 (10-8) 6-0.
MUGURUZA STUNNED
Muguruza's US Open campaign came to an end in the second round, sensationally upstaged 7-5 6-3 by Pironkova, who is playing her first tournament since Wimbledon in 2017.
Australian Open runner-up and two-time slam champion Muguruza was serving for the first set when the Spaniard started to unravel.
Pironkova, who gave birth to a son during her time away from the WTA Tour, took control at the end of a tight first set and never looked back.
"I'm not going to hide, I didn't expect my first tournament to be so good and to play so well. It's welcome! That's why I came back, for these matches and these stages," Pironkova said after winning 93 per cent of her first serves.
AZARENKA ROLLS ON
Former world number one and two-time Australian Open champion Victoria Azarenka topped fifth seed Aryna Sabalenka 6-1 6-3.
A US Open finalist in 2012 and 2013, Azarenka is in fine form after winning the Western & Southern Open last week.
And Azarenka is now just one victory away from her first second-week appearance at Flushing Meadows in five years.
Meanwhile, seventh seed Madison Keys also progressed to the third round.
Gauff reached the second week at Flushing Meadows in the women's singles for the first time after cruising to a 6-2-6-3 win over Madison Keys on Friday.
The number 12 seed saw off her fellow American in composed fashion to book her place in the last 16, exceeding her previous best result at the US Open in 2019.
Gauff was largely in control against the number 20 seed Keys to deliver near-flawless performance, chasing a second grand slam final of the year after finishing as runner-up at the French Open to Iga Swiatek.
She will face China's Zhang Shuai in the next round, but when asked if she will watch Williams' match against Ajla Tomljanovic later in the day during her on-court interview, Gauff said she would, adding: "It's been amazing watching Serena's matches so far. I don't know when I'd be due to face her but that's the goal.
"It's been a lifelong dream of mine to do that. Five years ago yesterday I was watching Venus and Serena play here. It's crazy to be on this court now.
"I tried to flex to my friends that I had courtside seats, now I'm on the court!"
Should both remain in the tournament, Gauff and Williams would face each other in the semi-finals.
Gauff also paid tribute to Keys, and to the crowd at Arthur Ashe Stadium, saying: "[The win] means a lot to me... I missed my alarm and was so late. I was here until 9pm last night and lost a doubles match [with Jessica Pegula].
"Kudos to my team, they got me up for it.
"I wasn't sure how the crowd was going to go. We all love Madison... I'm good friends with her off the court, but having support here meant a lot."
Vondrousova's topsy-turvy match against Katie Volynets started on Wednesday before concluding on Thursday, with the number five seed coming out on top 0-6, 6-1, 6-4.
The American started strongly, storming through the first set, but Vondrousova recovered well to take a commanding 4-1 lead before rain washed out the rest of the game.
Vondrousova picked up where she left off upon resumption on Thursday and won one game before another delay due to rain, but eventually saw out the win.
Keys, meanwhile, won in straight sets against Mayar Sherif, holding out for a 6-0 7-6 (9-7) victory.
The American cruised through the first game, enjoying three breaks, but a stern fightback from Sherif almost caused some problems.
Keys held her nerve though, avoiding a decider by saving three set points to prevail on Court Suzanne Lenglen.
Vondrousova will face Chloe Paquet in the next round, while Keys will play either Sara Errani or Emma Navaro.
Data Debrief: Vondrousova marches forward
The Roland Garros is the tournament where Vondrousova has won the joint-most career matches (13, equalling Indian Wells).
She is also unbeaten against opponents ranked above 100 in the WTA since the start of 2023, going 10-0 against such competitors.
Williams needed just 44 minutes to crush 18-year-old Amanda Anisimova 6-1 6-1 in their last four clash at the WTA International tournament in New Zealand.
The 23-time grand slam champion mixed 17 winners with six unforced errors and lost just nine points on serve. Williams served five aces and converted all five of her break points in a dominant display in the lead up to the year's first grand slam in Melbourne.
The American moved into her 98th WTA Tour final and will be aiming for a 73rd title but first since the 2017 Australian Open when she faces Jessica Pegula.
Pegula upset fifth seed Caroline Wozniacki 3-6 6-4 6-0 in their semi-final.
A two-time runner-up, Wozniacki – who will retire after the 2020 Australian Open – won just 10 points in the third set.
Wozniacki will contest the doubles final with Williams against Taylor Townsend and Asia Muhammad.
In Brisbane, Pliskova lost a first set on a tie-break in which she squandered two set points and saved four, and was staring down the barrel after Osaka broke for a 6-5 lead in the second.
However, Osaka's first serve on match point was overly tentative and a series of errors handed Pliskova the break back. The second seed took full advantage, winning the subsequent tie-break and taking the decider in comfortable fashion to defeat the reigning Australian Open champion 6-7 (10-12) 7-6 (7-3) 6-2.
Earlier, Madison Keys rallied past Petra Kvitova to clinch a 3-6 6-2 6-3 victory, meaning there will be no all-Czech final in Queensland.
At the Shenzhen Open, Russian Ekaterina Alexandrova clinched her maiden WTA Tour title with a 6-2 6-4 win over Elena Rybakina in the final.
French Open finalist Paolini progressed to the last eight with a 6-3 6-7 (6-7) 5-5 victory, though the Italian was on the brink of an exit before that.
The seventh seed trailed 5-2 in the deciding set before dragging back into the contest by winning two games, with Keys then calling for the physio and a medical time-out due to a thigh issue.
American Keys was visibly distraught after leaving the court for treatment, returning to concede another game and struggling to serve before retiring with the game finely poised.
Paolini will now face either Emma Navarro or Coco Gauff in the quarter-finals at SW19.
Data Debrief: Paolini's Italian pride
Paolini became the first Italian in the Open Era to reach the women's singles quarter-final at Wimbledon and Roland-Garros in the same season, having fallen in the French Open final to Iga Swiatek.
Having never won a match at Wimbledon before this year, Paolini has now won four straight, though this triumph came in unwanted circumstances.
Keys is only the second player in the Open Era to retire in the third set of a women's singles round-of-16 clash at a major, after Julie Heldman progressed past Billie Jean King via retirement at the US Open in 1973.
