Seventh seed Kasatkina had no answers in Stuttgart as she fell to a 6-1 6-1 defeat against Badosa, who recorded the ninth top-10 victory of her career and first in exactly 12 months.
Badosa has won 29 clay-court matches in the last three seasons – only Ons Jabeur (35) and Iga Swiatek (30) have won more – but the Spaniard had to enter this tournament as a wildcard.
The 25-year-old was as high as second in the world last year but has fallen to 31st, and she outlined her goal to reach the top once more after her first-round win set up an all-Spanish meeting with Cristina Bucsa.
When asked about her ambitions to return to the world's top three, Badosa said: "That's what I'm working on every day. That's one of my goals – I want to be back on the top.
"I like to play big matches, I like to be in the last rounds of the tournaments. I still know I have that level. I still know I was that player. I still believe in myself, and I hope I'm back there very soon."
Jelena Ostapenko eased into the second round with similar dominance after downing Raducanu 6-2 6-1 in just 58 minutes, teeing up a meeting with world number four Ons Jabeur on Wednesday.
Latvian Ostapenko powered 19 forehand winners and went unbroken, acknowledging in her on-court interview that familiar aggression was key to her success in the battle of two one-time grand slam winners.
"I knew against her the main thing was to step in the court," said former French Open winner Ostapenko. "I missed some balls, but I tried to be aggressive all the time when it was possible.
"Just try to take the ball early, don't give her many chances. And finally, I'm back on clay, my favourite surface."
Barbora Krejcikova was another straight-sets winner, scoring a 6-2 6-0 triumph over Liudmila Samsonova, with the reward for the 2021 Roland Garros champion being a tricky clash against second seed and Australian Open winner Aryna Sabalenka.
There was no such ease for Anastasia Potapova in a battling 6-3 3-6 7-6 (7-4) victory over Petra Martic, the Russian's ninth third-set win in 2023 – no WTA Tour player has managed more.
Tatjana Maria overcame Ylena In-Albon 6-2 4-6 7-6 (7-4) in another enticing clash, while Beatriz Haddad Maia advanced after Martina Trevisan was forced to retire when trailing 7-5 1-1 due to a right thigh injury.
The Australian started slowly in the quarter-final of the WTA 500 tournament on Friday as Pliskova broke her serve twice in taking the first set, before Barty hit back with three breaks of her own to force a decider.
Barty was two points away from losing on five occasions as world number nine Pliskova served for the match at 5-4 in the final set.
But she broke the Czech's resolve eventually, sealing victory when Pliskova hit the ball long after a baseline rally.
The win was Barty's eighth consecutive victory over a top-10 opponent and she said in a media conference afterwards that facing top players in the world brings the best out of her.
"When you come up against top-10 opponents, you have to go to that level above to be able to compete. They force you to bring your best," Barty said.
"With a lot of the girls in the top 10, we've had plenty of matches that have gone either way, different experiences, so each time I love that challenge of testing myself against the best."
Barty will face Elina Svitolina in the semi-finals after she saved two match points to claim a 6-7 (4-7) 7-5 6-2 victory over Petra Kvitova.
In the other half of the draw, Simona Halep breezed through to the semi-finals with a 6-1 6-4 win over Ekaterina Alexandrova.
Halep clinically closed out the first set, and although Alexandrova showed more fight in the second, the world number three did not allow her a route back into the match.
Halep will face Aryna Sabalenka following the Belarusian's 7-5 4-6 6-1 win over Anett Kontaveit.
In the Istanbul Cup, top seed Elise Mertens secured her place in the semi-finals with a 6-4 6-4 win over Katerina Siniakova.
Mertens will face Veronika Kudermetova who fought back from a set down to clinch a 2-6 6-3 6-3 win over Ana Bogdan.
The other semi-final will see Sorana Cirstea play Marta Kostyuk. Cirstea progressed after Fiona Ferro, trailing 6-4, retired through injury while Kostyuk beat Ana Konjuh 7-5 4-6 6-3.
The world number one was given a much sterner test by the former champion in the second set but won all 24 points when landing her first serve and had 19 winners to her name.
Next up for the amiable Australian is a meeting with either Jelena Ostapenko or Karolina Pliskova, who made it through to the round of 16 on Wednesday as did Angelique Kerber and Marketa Vondrousova.
Defending champion Petra Kvitova, seeded sixth, had to overcome a second-set blip to earn a 6-3 3-6 6-3 triumph over Maria Sakkari and a spot in the quarter-finals.
Anett Kontaveit continued her love affair with the tournament, upsetting third seed Sofia Kenin 7-5 6-4. She has now reached the quarter-finals or better in each of her four visits to Stuttgart – including a runner-up finish last season.
At the Istanbul Open, seeded pair Daria Kasatkina (4) and Wang Qiang (8) were ousted by Marta Kostyuk and Ana Konjuh respectively in the round of 16.
Katerina Siniakova and Sorana Cirstea both made the quarter-finals, while Kaia Kanepi was a last-32 victor over Zarina Diyas.
The world number 12 eased to a 6-4 6-2 victory over the 17-year-old qualifier, who saved five match points in her final service game before Bencic closed things out.
"My love affair with clay is... I'm trying to improve myself on it," Bencic said after her first-round triumph.
"I think I'm getting better and I'm taking falls sometimes. I'm trying my best on this surface."
Maria Sakkari was similarly comfortable in progressing to the next round, hitting 24 winners as she dispatched Andrea Petkovic 6-2 6-2 on her debut at the tournament.
At the Istanbul Cup, four of the five scheduled matches were completed before rain stopped play with Anastasia Pavlyuchenkova and Anastasia Potapova level at a set apiece.
Eighth seed Wang Qiang fought back from a set down to beat Anastasia Gasanova 4-6 6-1 6-2.
There were also wins for Ana Konjuh, Katerina Siniakova and Viktorija Golubic.
The Czech left-hander was the last winner of the German tournament, beating Anett Kontaveit in the 2019 final, with last year's event cancelled due to the pandemic.
Kvitova was handed a tough opening assignment against Australian Open runner-up Brady, but the American's streak of defeats since that Melbourne final defeat extended to three as Brady lost 6-4 6-3 in an hour and 32 minutes.
Two-time former Wimbledon champion Kvitova, seeded seventh, picked apart the Brady serve once in each set and fended off three break points across the contest to secure her last-16 place.
She was joined in the second round by powerful Belarusian Aryna Sabalenka, as the fifth seed scorched to a 6-2 6-2 win over China's Zhang Shuai.
Earlier, Ekaterina Alexandrova, Kontaveit, Anna Lena Friedsam and Laura Siegemund also went through to the last 16 of the WTA 500 event.
Meanwhile, Fiona Ferro caused a shock at the Istanbul Cup as she landed a 7-5 6-2 first-round win over former champion Petra Martic.
Martic, seeded second this year and ranked 21st in the world, landed the title in Istanbul in 2019 but was rolled over by French player Ferro in an hour and 45 minutes, in a match featuring seven breaks of serve.
Veronika Kudermetova followed her recent maiden title in Charleston with a nerve-jangling first-round win against Bernarda Pera, the fifth seed scrambling through 6-4 3-6 7-6 (7-4).
There was no such toil for top seed Elise Mertens, a 6-2 6-0 winner against Lara Arruabarrena, or for Daria Kasatkina, who dished out a 6-1 6-0 drubbing to Tereza Mrdeza.
Kasatkina is seeking her third title of 2021, having won previously in Melbourne and St Petersburg.
Anastasia Pavlyuchenkova bowed out of the WTA 250 event though, beaten 7-6 (7-2) 6-7 (8-10) 6-4 by compatriot Anastasia Potapova.
US Open champion Raducanu overcame Tamara Korpatsch 6-0 2-6 6-1 to set up a meeting with world number one Swiatek.
It will be the pair's first meeting on the WTA Tour and Raducanu's maiden encounter with a top-10 opponent.
The Briton, who is playing her first Tour-level clay-court event, won 90 per cent of points on her first serve in the opening set but that slipped to 56 per cent as she opened the door to a comeback in the second.
However, Raducanu rediscovered her composure in the decider and got over the line after an hour and 39 minutes.
Fourth seed Sakkari retired while 6-4 3-1 down to home hope Laura Siegemund, who will take on Liudmila Samsonova after she bested Pliskova 6-4 6-4.
Paula Badosa came through a third-set tie-break to beat Elena Rybakina 6-2 4-6 7-6 (7-4) and Aryna Sabalenka put a spanner in the works of Bianca Andreescu's comeback by taking their match 6-1 3-6 6-2.
Ons Jabeur beat Daria Kasatkina and Anett Kontaveit eventually ousted Ekaterina Alexandrova in a tie-break finale after surrendering the first set.
At the Istanbul Cup, third seed Veronika Kudermetova was granted a walkover against Ana Bogdan.
Seeds Ajla Tomljanovic (6) and Sara Sorribes Tormo (7) got past Lesia Tsurenko and Varvara Gracheva respectively, while there were also wins for Yulia Putintseva and Anastasia Potapova.
Lucky loser Parks hit eight aces but also 11 double-faults and was undone once in each set as Zheng took a straight-sets victory to tee up a second-round clash with the world number one.
Cristina Bucsa came up with a third-set bagel to join Zheng in round two, having initially made hard work of fellow qualifier Tamara Korpatsch in her 3-6 6-4 6-0 win.
Bucsa will meet the winner of the clash between seventh seed Daria Kasatkina and last year's semi-finalist Paula Badosa.
Meanwhile, Donna Vekic will take on either Karolina Pliskova or Maria Sakkari after she battled to a 7-6 (9-7) 7-6 (7-5) triumph over Ekaterina Alexandrova.
The star-studded line-up sees grand slam winners including Emma Raducanu, Barbora Krejcikova and Jelena Ostapenko get their campaigns underway on Tuesday.
Ons Jabeur, who claimed victory at the Charleston Open earlier this month, kicks off her tournament on Wednesday.
Swiatek made a disastrous start, going 4-0 down, and though she broke back once, was unable to find the second as Pliskova took the opening frame 6-4.
The determined Pole stepped up a level though to take the second 6-1, before breaking early in the third.
It was still an improvement for the Czech player, who lost 6-0 6-0 to Swiatek in their only previous meeting in Rome in 2021.
Pliskova kept her opponent honest on her own serve, but Swiatek had too much for the world number 17 as she clinched the decider 6-2.
Aryna Sabalenka also showcased her powers of recovery as she beat Paula Badosa despite going a set down.
The second seed won 4-6 6-4 6-4 in an even contest that saw nine breaks of serve, before the Belarusian eventually got over the line.
Sabalenka is now the player with the joint-most comeback wins over the last two seasons (13) level with Caroline Garcia, though the French star was actually the victim of a comeback herself on Friday.
Garcia won the first set against Anastasia Potapova, before the Russian came back to take it 4-6 6-3 6-3 to set up a semi against Sabalenka.
There was no need for such drama from Ons Jabeur, who eased to a 6-3 6-0 victory against Beatriz Haddad Maia in just 68 minutes to confirm a clash with Swiatek.
Swiatek had not played since sustaining the issue in the semi-finals of Indian Wells over a month ago, but advanced on Thursday despite stating that she felt "rusty".
The world number one won 84 per cent of points after landing her first serve in as she made up for lost time.
Swiatek also forced eight break points, winning four of them as she took just and hour and 26 minutes to set up a quarter-final with Karolina Pliskova, who bested Donna Vekic in a thriller.
Pliskova looked to be on her way to a routine win as she claimed the first set 6-2, only for the Croatian to take the second via a tie-break.
The decider also went the distance, with Pliskova able to finally put Vekic away 6-2 6-7 (5-7) 7-6 (7-5) to book her clash with Swiatek.
Coco Gauff perhaps paid the price for taking almost three hours to beat Veronika Kudermetova on Wednesday, as the fifth seed fell to a straight-sets loss to Anastasia Potapova on Thursday, going down 6-2 6-3.
Fourth seed Caroline Garcia will go up against Potapova next after she defeated Tatjana Maria 7-6 (7-5) 6-4, while Paula Badosa had few problems seeing off fellow Spaniard Cristina Bucsa 6-1 6-2 and will face second seed Aryna Sabalenka in the last eight.
Since Russia launched its assault in February 2022, supported by Belarus, many sports have banned athletes from the two countries outright, while tennis has been among those that has largely allowed them to compete but under a neutral flag.
Swiatek, the women's tennis world number one, hails from Poland and has been a vociferous critic of the war and a fervent supporter of Ukraine.
Interim recommendations were issued by the IOC last month to international federations and organisers of events regarding the involvement of Russians and Belarusians.
The Olympic body urged federations to exclude any athletes or support personnel "who actively support the war" and said teams from either country should not be allowed to compete in international sport for now.
However, in a statement, the IOC said it should be "the sole responsibility" of sporting bodies to decide whether individuals can compete, and this should be "based on their sporting merits and not on political grounds or because of their passports".
There is a clear possibility of Russian and Belarusian athletes being allowed to compete as neutrals at the Paris 2024 Olympics, although IOC president Thomas Bach stressed there has been no decision taken on that matter.
Swiatek was asked about the IOC stance after her opening match at the Stuttgart Open, and the 21-year-old said: "Human rights are important, but I always feel like there are values that you have to kind of treat respectfully, and war is not something that we want in the world. I was pretty open about that since the beginning.
"Right now the situation is pretty complicated, because at the beginning of the war there weren't many decisions one way. At first they were kind of banned in other sports, not in tennis.
"Then it changed a little bit, and they are starting to be allowed, the Russian and Belarusian players, which is pretty confusing, because I feel like nothing changed in Ukraine and the cities are still under attack and many Ukrainian athletes are fighting in the war and actually losing their lives.
"It's heartbreaking. I just hope, no matter what the decision is going to be, the sport will be able to kind of put people together and not separate them.
"But there are tensions, so it may be tricky and hard to do. As just one athlete, I don't have full influence on what's going on, so we kind of have to just compete our best no matter what the circumstances are."
The world number one has seen her dominance take a dip this season, with Sabalenka and Elena Rybakina emerging as serious candidates to displace her at the top of the women's game.
However, Swiatek is the queen on clay and illustrated her prowess with a 6-3 6-4 win at the tournament that rewards its champion not only with a cheque for $120,150 and trophy, but also a Porsche.
This success made Swiatek the first player to defend the Stuttgart title since Angelique Kerber's back-to-back 2015 and 2016 triumphs, and it came in her first tournament back after a rib injury.
The 21-year-old Polish player entered the title match having said she and Ons Jabeur are the tour's best players on clay, and that put her there to be shot at by Australian Open winner Sabalenka, who has climbed to second place in the rankings.
This was the first time a tour-level final has featured the top two women in the world rankings since the 2018 Australian Open final, when Simona Halep beat Caroline Wozniacki.
It was also a repeat of last year's Stuttgart final that Swiatek won comprehensively, dropping only four games, amid a 37-match winning run that would bring her a second French Open title.
The traffic was not quite so one-way this time, but Swiatek was terrific and did not drop serve once.
For Sabalenka, the outcome meant a third consecutive defeat in Stuttgart title matches, having also lost in the 2021 showpiece to Ash Barty.
After Swiatek surged through the opener, she forced a break point at the start of the second set and a Sabalenka double fault handed over the advantage.
Unforced errors were costing the Belarusian, who could not capitalise on a break point in the fourth game of the second set, going on to fling a desperate forehand wide to hand over a 3-1 lead.
Swiatek took evasive action to avoid a fierce Sabalenka smash in the next game, after initially charging towards the net, but she remained firmly in charge.
The title was secured with a ruthless love game on serve, an outmanoeuvred Sabalenka left to watch her opponent drill away a backhand into an empty court.
Reflecting on her injury lay-off, Swiatek said: "It's been such an intense time in the last couple of weeks and tough decisions sometimes, but I'm so happy we're making the right decisions."
Sabalenka, who during the week made no secret of her eagerness to win the Porsche, said: "I'll keep coming back until I get the car."
The world number one overcame Australian Open champion Aryna Sabalenka 6-3 6-4 to become the first back-to-back winner of the Stuttgart crown since Angelique Kerber (2015 and 2016).
Swiatek, who was appearing in her first tournament after a rib injury, claimed her second silverware of the season, in which she also completed a successful title defence in Doha.
The Pole has plenty of ranking points to defend this term having won eight titles during a dominant 2022 campaign.
Swiatek was also a finalist in Dubai and, despite a fourth-round exit at the Australian Open, she is pleasantly surprised to have started 2023 in a similar vein of form.
"Honestly, the beginning of the season was so tough that I'm happy to be in that place now," Swiatek said during her post-match press conference.
"I just hope I'm going to continue having that good mindset without looking at all this stuff [defending points]. I was able to do that here. I really like playing on clay, so I just hope I'm going focus on just playing.
"I'm just pretty proud of my consistency, because when I was consistent on another level, it was nice, but this level, it's even over my expectations.
"Last year was really, really tough, and I felt like this season may be tough because of what people are saying and expectations from the outside. Also, I knew how it is to win these tournaments in a row.
"Now, I feel like I just can use my experience a little bit more. I'm just happy that I'm world number one for more than a year, and it's an exciting time."
World number one Swiatek was 3-0 up against Jabeur when her tearful opponent called a medical timeout and ultimately ended the contest early.
It sets up a mouthwatering showdown between top seed Swiatek and second seed Sabalenka, who defeated Anastasia Potapova in straight sets earlier on Saturday.
Jabeur, who struggled to shake off the injury sustained in the first game, said: "The third point, I don't know what happened.
"I was really excited to play Iga today – it's always a fun match between us. I wish her the best luck for the final. I'm sorry guys, I really tried to run, but Iga never makes it easy."
Sabalenka, a beaten finalist in the past two years, held her serve in the opening set against Potapova and twice broke her unseeded opponent to take the lead.
The Belarusian raced 4-0 ahead in the second set and saw out a comfortable 6-1 6-2 victory in a little under an hour to reach her fourth final of the year.
"I think I was really focused, and I think from the very first point I was playing really aggressive," Sabalenka said in her on-court interview. "I didn't give [Potapova] much time.
"I think that's why the match finished like that quick. But anyway, she's a great player, and I think in the future she's going to be a top player."
Swiatek defeated Sabalenka in last year's Stuttgart final 6-2 6-2 and is aiming to become the first player to defend the title since Angelique Kerber in 2016.
The WTA Tour's top-ranked player earned $120,150 for winning the title at the Stuttgart Open last week, plus a Porsche sports car, when she beat Australian Open champion Aryna Sabalenka in the final.
Yet for taking the title at the Barcelona Open in the same week, a cheque of €477,795 ($527,000) went to Carlos Alcaraz.
Those tournaments are considered comparable in terms of status and the quality of their fields, yet the difference between the money on offer was striking.
It offered a reminder of the gap between the elite men and women at regular tournaments, despite grand slam events offering equal rewards.
Swiatek and Alcaraz both compete this week at the Madrid Open, where prize money for men and women is equal, the champion of each event collecting €1,105,265 ($1.2m).
Asked about last week's situation, Swiatek said: "Well, it's kind of obvious what my opinion is, because tennis is one of the sports where we speak about equality. I think it's better than most sports anyway.
"But still, there is a lot we can work on in terms of getting equal prize money on some WTA tournaments compared to ATP on the same level.
"Grand slams are already even, as we know. That's nice, but for sure it would be good if WTA would focus on that, but I don't really want to get into that, because it's a lot of business and sometimes politics.
"I don't think I have a lot of influence. I just can say that it would be nice for our sport if it was equal, especially because we kind of do the same work."
The 21-year-old Polish player defended the women's game as she said: "I also get people who are saying that men's tennis is nicer to watch and guys can do more because they are physically and biologically stronger.
"I think there were a lot of people, for example a couple of years ago, who were saying that WTA is not consistent and that's a shame and it should be better, but right now basically I think we are even more consistent than the guys with our game.
"Watching women's tennis gives the same emotions, and sometimes even more emotions, because we are women and we are a little bit more emotional. But, yeah, I think it would be nice if WTA could make it even."
