The world number 26, who was defeated by Amanda Anisimova in the Melbourne Summer Set 2 semi-finals last week, beat second seed Muguruza 6-4 6-4.
Kasatkina held throughout the opening set, landing 67 per cent of her first serves, and saw the job through in the second despite a couple of early breaks for Muguruza.
It is the Russian's first win over a top-five opponent since beating Caroline Wozniacki at the 2018 French Open.
She will now face fifth seed Paula Badosa, who saw off Olympic gold medallist Belinda Bencic 7-6 (8-6) 3-6 6-3 in an entertaining match lasting two hours and 35 minutes.
The other semi-final in Sydney will be contested between Anett Kontaveit and Barbora Krejcikova, who advanced past Ons Jabeur and Caroline Garcia respectively.
Krejcikova proved far too strong for Garcia, prevailing 6-0 6-2 in 70 minutes, while Kontaveit was in action for just 43 minutes before being handed a walkover win in her match.
Jabeur had targeted "payback" against Kontaveit after her quarter-final opponent pipped her to the final WTA Finals spot in November, but injury cost her the chance to do so.
Having lost the first set 6-4, Jabeur – who eliminated Petra Kvitova in the previous round – felt unable to continue due to a lower back injury.
At the Adelaide International 2, three of the five Americans in action made it through to the semi-finals.
Alison Riske's clash with compatriot Madison Brengle ended early due to the latter retiring with the first set level at 3-3. Tamara Zidansek awaits Riske after beating Lauren Davis 7-6 (7-4) 7-6 (9-7).
Coco Gauff and Madison Keys will meet in the other semi-final, meanwhile, following victories over Ana Konjuh and Ludmilla Samsonova in two and three sets respectively.
Badosa, who made this year's French Open quarter-finals, squandered two match points at 5-2 in the second set against three-time grand slam champion Kerber before steadying to secure her fifth final-four appearance of the season on Thursday.
In the semi-finals, Badosa will face Tunisian 12th seed Ons Jabeur, who got past Anna Kontaveit in straight sets, confirming her historic rise into the top 10 of the rankings, as the first-ever Arab player to achieve the singles feat on either the WTA or ATP Tour.
KERBER TOPPLED BY BADOSA
Former world number one and 10th seed Kerber bowed out at Indian Wells, with Badosa triumphing 6-4 7-5 in 86 minutes.
In her Indian Wells debut, 21st seed Badosa responded strongly after fluffing two match points to become the first Spanish woman to make the event's semi-finals in 18 years.
"It sounds amazing," Badosa said during her on-court interview. "The second set was very mental. I wanted this match so badly. I got super nervous.
"For one second I thought who was on the other side of the net and I got more nervous against a three-time grand slam champion. It means a lot to me. It's amazing."
In the first set, Badosa broke Kerber at 4-4 before serving out the opening set where she was excellent on her first serve, staving off the German's only two break points.
The Spaniard raced to a 5-2 lead in the second set and had two match points on Kerber's serve. The experienced Kerber responded by holding serve and then breaking back, before levelling at 5-5.
But Badosa showed her mettle by winning the final two games, breaking Kerber for victory as she upped her level.
JABEUR SEALS TOP-10 BERTH WITH TRIUMPH
Jabeur defeated Estonian 18th seed Kontaveit 7-5 6-3 to move into the top 10 for the first time in her career.
The Tunisian will become the first Arab player to make the top 10 when the updated WTA rankings are made official on Monday, but she also qualified for the biggest semi-final of her career to date.
"It feels amazing," Jabeur said. "We've been working hard since years. When I spoke at the end of last season, I said I wanted to be in the top 10. People doubted us as a team, we proved them wrong.
"Being a top 10 means a lot but we're not going to stop here. We're going to go further hopefully."
Jabeur, who made this year's Wimbledon quarter-finals, triumphed in 86 minutes, although she did not have it all her way, in a match full of momentum swings.
The 27-year-old Jabeur had been a double break up at 4-1 in the first set before Kontaveit hit back to level at 5-5, only for her to break back immediately and serve out the set.
Jabeur broke Kontaveit to love at 3-3, rattling off the final three games, including two breaks, to secure victory and keep alive her hopes of making the WTA Finals.
Kerber made home advantage count, following up a 2-6 6-3 6-3 quarter-final win over Amanda Anisimova – a match that was pushed back from Thursday when rain washed out play – with a triumph over top seed Petra Kvitova.
The former world number one came back from behind to win 3-6 6-4 7-6 (7-3) and take a spot in her first WTA singles final since 2019.
Kerber and Kvitova have now met 15 times, with the German winning on nine occasions.
She will go up against an unexpected finalist in the form of Siniakova, who defeated Sara Sorribes Tormo.
The Czech is the world number two in doubles, winning three grand slam titles in that format, and will be looking to replicate the feat of her regular partner Barbora Krejcikova, who triumphed at the French Open this year.
At the Viking International in Eastbourne, Jelena Ostapenko made light work of Elena Rybakina, while Anett Kontaveit made it into the final due to Camila Giorgi's retirement.
Latvian wildcard Ostapenko finished her 6-4 6-1 victory with zero double faults – the first time she has managed such a performance since winning in Luxembourg two years ago.
"I'm really happy with the way I played this week, and every match I played better and better," Ostapenko told a news conference after clinching a spot in her ninth career final.
"It's been a while [since making a] final, so I'm really happy to be in a final and looking forward to tomorrow's match."
The 2017 French Open champion will face Estonia's Kontaveit, who has won their previous two meetings and was 5-4 up in the opening set against Giorgi when her opponent retired hurt.
"It's actually nice to have a Baltic final, because [we're] not such big countries, but we still have good players," Ostapenko added.
"Anett, I know since juniors. We have been playing a lot, maybe not so many matches but we practice sometimes together, in juniors, and played even doubles. So I know her quite well."
Kontaveit overcame top seed Petra Martic 6-2 6-4, before Ferro sank Italian title hopes in Sicily with a 2-6 6-2 7-5 win over Camila Giorgi.
Fourth seed Kontaveit is ranked seven places below world number 15 Martic and she won impressively in an hour and 29 minutes.
The Estonian will be targeting just a second career singles title and a first on clay, having previously won on grass in 2017 at Rosmalen.
She said: "I felt like I played a very good match today. I was quite aggressive, consistent, and I served especially well in the first set. It got a bit close in the end, but I played a good game at 5-4 and I'm happy to be in the final."
Martic called the match "a tough one" and spoke of missing chances to make the scoreline tighter than it became.
Ferro and Giorgi slugged it out for two hours and six minutes before their clash produced a finalist, with the home player falling agonisingly short.
World number 53 Ferro go after her second WTA title. Her first also came on clay at Lausanne in July last year.
The 2020 tennis season was suspended for almost five months amid the coronavirus pandemic, and the women's tour has returned with fans in Italy, socially-distanced crowds having been in attendance all week in Palermo
Top seed Kontaveit overcame world number 61 Irina Bara in straight sets in her first-round clash and third favourite Krejcikova followed suit in her second-round match against Poland's Magdalena Frech.
Kontaveit will meet Sweden's Rebecca Peterson in the next round as she looks to set up a quarter-final meeting in Germany with eighth seed Andrea Petkovic, who defeated Misaki Doi 6-4 6-3 on Tuesday.
There was no such luck for ninth seed Elena Gabriela Ruse, though, after she lost 6-0 6-4 to last week's Budapest Grand Prix winner Bernarda Pera.
Swiss Joanne Zuger will next be the next challenge for Pera as she aims to reach a quarter-final clash against Katerina Siniakova, who triumphed 6-1 6-1 over Brazil's Laura Pigossi.
Putintseva is ranked as the second favourite in Italy and progressed with ease from her first-round clash against world number 147 Jaimee Fourlis, winning 6-3 6-1.
Seventh seed Anna Bondar had little difficulty beating Clara Burel 6-4 6-4, though Caroline Garcia and Nuria Parrizas Diaz faced more difficult tasks in their respective openers.
France's Garcia, the fifth favourite in Palermo, responded to a first-set scare to defeat compatriot Chloe Paquet, while eighth seed Parrizas Diaz also lost her opening set before downing Asia Muhammad.
Champion in St Petersburg two weeks ago, Kontaveit extended her winning run to eight matches following a 6-4 6-1 success.
The opening set was neck and neck until Kontaveit won 15 out of 16 points from 30-30 at 4-4 to draw first blood and establish a 2-0 lead in the second.
The Estonian, who registered just 12 unforced errors throughout the contest, then took 12 of the last 15 points to advance to the last four.
"At times, it was just kind of fun because I felt like the level was really good, and I was playing really well," said Kontaveit, who has won nine of her last 13 matches against top-10 opposition.
"I think I have this confidence that I can go deep every week that I'm playing, and I'm not setting these mental barriers to myself that I used to do.
"I'm very happy with being in the semi-finals, but I also feel like I can still go deeper, I can still do more. So, I'm not too satisfied yet with this result. I feel like if I play well or if I'm consistent, I have a chance with anyone.
"I'm really happy that I'm bringing a good level of tennis consistently every tournament. I think that's something that I'm just most pleased with."
In the semi-finals, Kontaveit will face another in-form player in Jelena Ostapenko, who saw off Garbine Muguruza in straight sets.
Having triumphed in Dubai last week, the 15th seed has now recorded nine successive victories for the first time in her career after prevailing 6-2 6-2.
Ostapenko struck 39 winners and claimed 15 of 18 points on her opponent's second serve as she moved a step closer to a maiden title in Doha, having reached the final six years ago.
Meanwhile, Iga Swiatek is through to her first WTA 1000 semi-final on a hard court after a 6-2 6-3 win over Aryna Sabalenka.
The former French Open champion won seven out of eight breakpoints, while reeling off six successive games in the second set to secure a comfortable victory.
Next up for her is Maria Sakkari, who recorded her third win against Coco Gauff in four meetings after prevailing 6-3 6-3.
The sixth seed is through to her sixth semi-final at WTA 1000 level or above – and targeting her first such title.
Third seed Kontaveit, who won this competition last year, retired when a set down to Tereza Martincova, while world number seven Maria Sakkari was defeated 5-7 7-5 7-5 by 21-year-old American Alycia Parks in a big upset.
Parks lost the opener but found two crucial breaks of serve when 6-5 up in both the second and third sets to eliminate the fourth seed.
The withdrawal of Belinda Bencica – seeded sixth – with a foot injury put Barbora Krejcikova into the quarter-finals, while Ekaterina Alexandrova will also be in the last eight after overcoming fifth seed Daria Kasatkina 6-1 7-6 (7-1).
The tournament favourites were in much better form at the Jasmin Open in Tunisia, as the top two seeds sealed their places in the quarter-finals with straight-sets wins.
Favourite Ons Jabeur cruised to a 6-1 6-3 victory over Evgeniya Rodina, converting four of her seven break points to safely advance to the next round of her home tournament.
And number two seed Veronika Kudermetova eased past Magdalena Frech 6-3 6-4 to set up a quarter-final meeting with Diane Parry.
Swiatek advanced to the Doha showpiece for the first time after managing her first win over Sakkari in four attempts with a 6-4 6-3 triumph on Friday.
The Pole was in imperious form as she delivered 20 winners to overcome sixth seed Sakkari in an hour and 28 minutes, collecting her seventh top-10 win and second straight such win after defeating Aryna Sabalenka in the quarter-finals.
The seventh seed will now meet Kontaveit, who continued her impressive streak with a 6-1 6-4 win over Ostapenko in just 68 minutes.
Ostapenko headed into the clash on a career-best nine-match winning run, but succumbed to her fourth loss in five meetings with the fourth seed in Qatar.
Ostapenko did have back-to-back break points at 5-5 in the final set, but Kontaveit managed to hold on for victory.
"She can outplay anyone, and then she might not find the consistency sometimes, so you have to be ready for that," Kontaveit said of Ostapenko.
"I was trying to play a consistent match and just do my best on my serve and hold on to it, especially in the second set when I was a break up.
"Sometimes when she's on fire, her returns are unplayable and it's just very difficult.
"But I kept repeating to myself, 'I'm really good at serving it out, I'm really good at serving it out,' and eventually managed to do that.
"How you approach the match, how you're approaching the service games, I think if you're trying to be aggressive [...] that has a lot of effect on the serve."
It will be the seventh final that Kontaveit has contested since last August, converting those appearances into five titles so far. Kontaveit and Swiatek share a pair of wins apiece in previous clashes.
The Estonian, ranked ninth in the world, won her sixth career singles title after recording a tense 5-7 7-6 (7-4) 7-5 win over her Greek rival, in a clash between the tournament's top two seeds.
The victory means Kontaveit leads Sakkari for head-to-head victories, winning seven of their 13 meetings to date, and stretched the champion's remarkable run of indoor wins to 20 matches.
She was made to suffer before recording her first title of 2022, winning the eagerly awaited clash after a gruelling three hours of tennis.
Sakkari struck the first blow, winning a tense opening set as she targeted a first WTA 500 title of her career.
Kontaveit responded strongly and forced a decider by winning a tight second via a tie-break.
Greek top seed Sakkari found herself one service game from victory after a strong start to the third set, before Kontaveit's counter-attack arrived.
Kontaveit rallied after going 5-3 down by registering consecutive breaks, before comfortably seeing out her final service game, and has now won five of her last six singles finals.
The in-form Wang made life difficult for top seed Kontaveit initially, impressively taking the first set against the world number four.
Kontaveit then appeared to be cruising to victory when she took the second set 6-2 and found herself 5-1 up in the third, but Wang staged something of a revival.
Wang won four games on the trot to stun Kontaveit, only for the 21-year-old to lose her nerve as her opponent broke again and then served out the match 3-6 6-2 7-5, taking her through to face Tereza Martincova.
Beatriz Haddad Maia was also caused problems by a Chinese player, with Xinyu Wang taking the third seed to three sets.
Haddad Maia took the first set fairly comfortably but was blown away in the second before her composure returned in the decider, winning 6-3 1-6 6-4 to also progress to the last 16.
The other seed in action on Tuesday was Jil Teichmann, and she had no such issues seeing off Laura Siegemund 6-4 7-6 (9-7), although the day's most impressive win saw Donna Vekic thrash Maileen Nuudi 6-2 6-0.
At the Parma Ladies Open, second seed Martina Trevisan was stunned 7-5 6-0 by Sara Sorribes Tormo.
It was a bad day for seeds throughout the draw in Italy. Anna Bondar (fifth), Nuria Parrizas Diaz (seventh) and Lucia Bronzetti (eighth) all lost in straight sets.
Third favourite Irina-Camelia Begu did buck that trend, however. She benefited from Viktoriya Tomova retiring, although the Romanian was already a set and 5-1 up.
The 26-year-old won five out of the final six games as she stormed to the first set, before securing her place in the quarter-finals with a superb second set in which she broke Martincova four times.
Fellow Estonian Kaia Kanepi is also through to the quarter-finals after a 7-5 7-5 victory over Ann Li.
The world number 32 found a crucial break with the opener tied at 5-5 as she took the first set, before breaking Li three times in the second to seal the win.
Eighth seed Shuai Zhang was dumped out by Donna Vekic in a 6-2 6-4 defeat, while fellow seed Jil Teichmann also saw her tournament ended as Ysaline Bonaventure beat her 7-6 (10-8) 6-3.
At the Parma Ladies Open, top seed Maria Sakkari came from a set down for the second consecutive match to overcome Maryna Zanevska and reach the semi-finals.
Zanevska sparked hopes for an upset as she broke the world number seven three times on her way to taking the opening set.
But Sakkari improved in the second to tie the match, before overcoming two breaks of serve from her Belgian opponent to win six of the last seven games and earn a 2-6 6-4 6-4 success.
Sakkari will face Danka Kovinic in the semi-finals, after the 27-year-old's 6-4 6-4 triumph over Italian Jasmine Paolini.
Irina-Camelia Begu's run of 12 consecutive wins on clay came to an end as she was defeated 6-2 7-6 (8-6) by Ana Bogdan in an all-Romanian clash.
Bogdan's opponent in the final four will be Mayar Sherif, who beat American Lauren Davis 7-6 (7-2) 6-3.
Kontaveit faced second seed Kvitova having previously toppled Paula Badosa and Belinda Bencic in straight sets.
Her last-four victory was even more comprehensive, as Kvitova went down 6-0 6-4 in 71 minutes.
Kontaveit advances to her fourth final of 2021 and avoids facing Iga Swiatek, who defeated her at the US Open – her only loss since winning the Tennis in the Land title last month.
But the Estonian must take on the woman who knocked her out of the Olympic Games in Maria Sakkari.
Number four seed Sakkari took down top seed Swiatek 6-4 7-5 to make her first WTA Tour final since 2019.
Sakkari had lost nine consecutive semi-finals since then, while Swiatek had never lost at this stage of a tour-level event, but the Greek was a deserving victor.
Kontaveit had failed to win a tournament since her maiden WTA Tour triumph in 's-Hertogenbosch back in 2017 before defeating Begu 7-6 (7-5) 6-4.
The world number 30 from Estonia had lost two finals this year, but she was not to be denied in Cleveland.
Begu fought back from 5-2 down in the first set to force a tie-break, but one mini-break was enough for second seed Kontaveit to take a big stride towards an elusive title.
The composed Kontaveit did not face a break point in a tight second set, not allowing her Romanian opponent a look-in as she served superbly.
Kontaveit only had one break-point opportunity of her own, but grasped it to lead 2-1 and went on to seal a confidence-boosting triumph ahead of the US Open.
Sam Stosur will be Kontaveit's opponent in the first round at Flushing Meadows, while Begu faces Andrea Petkovic.
On home soil, the top seed won 80 per cent of total service points in the opening set but Bonaventure fought back in the second to send the match to a deciding set.
A valiant effort from Kontaveit in the third set secured a spot in the final four, where she will face compatriot Kaia Kanepi after her 6-2 3-6 7-6 (8-6) victory over Karolina Muchova in the final match of the day.
Earlier on Friday, second seed Belinda Bencic defeated Donna Vekic to set up a semi-final clash against Barbora Krejcikova, who defeated Beatriz Haddad Maia in straight sets.
At the Parma Ladies Open, the scheduled semi-finals were postponed due to rain and will instead be played on Saturday, with the final to follow later in the day.
Top seed Maria Sakkari faces Danka Kovinic, with play to begin at 10:30 local time, and will be followed by Ana Bogdan against Mayar Sherif.
World number two Kontaveit recorded a 6-3 6-2 victory over Peterson on the clay in Germany, setting up a last-eight meeting with eighth seed Andrea Petkovic.
The Estonian's win was her third over Peterson and maintained her 100 per cent career record against Swedish opponents, taking her to seven such successes.
Kontaveit was joined in the quarter-finals by fellow seeds Aliaksandra Sasnovich, who beat Aleksandra Krunic 6-3 6-2, and Maryna Zanevska, who downed Alexandra Cadantu-Ignatik 6-4 6-1.
They will face off for a semi-final spot on Thursday, while Anastasia Potapova will meet 2021 French Open champion Barbora Krejcikova after beating Maria Carle in straight sets.
At the Palermo Ladies Open, meanwhile, third seed Zhang withdrew from her last-16 clash with home favourite Jasmine Paolini before taking to the court, citing an unspecified injury.
Fellow seeds Sara Sorribes Tormo and Anna Bondar both reached the quarter-finals with straight-sets wins, however, with the pair set to face off for a semi-final berth on Friday.
The unseeded Estonian, who is ranked 30th in the world, saw off fourth seed Sakkari 6-2 7-5 to claim the trophy in the Czech Republic.
Kontaveit has now won two tournaments in four weeks, having won in Cleveland last month to end a four-year wait since winning her first title in 2017.
This was Sakkari's first final in over two years as well, but Kontaveit cruised past the Greek in just over an hour and a half as she did not drop a set all week.
That flawless level of tennis saw her eliminate Petra Kvitova, Paula Badosa and Belinda Bencic en route to the final, where the 25-year-old faced only one break point as she powered to a comfortable victory over a player who reached semi-finals at the French Open and US Open this year.
Sakkari managed more of a fight in the second set, where she battled for her sole break point, but Kontaveit breezed past any pressure and kept her serve to maintain control.
Sakkari, who is likely to move into the top 10 despite losing, had boasted a 5-3 head-to-head record in main-draw clashes between the pair coming into Sunday's final, but 23 unforced errors outnumbered the 20 winners from her racket as Kontaveit collected her most notable title to date.
Kontaveit, seeded eighth, was made to work hard for victory by her Russian opponent, who had opened a 5-2 lead in the third set before being pegged back for a deciding tie-break.
Estonian Kontaveit saved two match points in the breaker, ultimately prevailing in two hours and 14 minutes to set up a second-round clash with Sara Sorribes Tormo after her 6-1 6-3 victory over Magda Linette.
"I was so close to being out, so I just tried to stay in the match," Kontaveit said. "I never really gave up. I tried to be a little more aggressive when I was down. I felt maybe I'd taken a little bit off my shots.
"She was really getting on top of me so I felt I had to push back, and sometimes when you take those risks they pay off.
"I think it was more adrenaline and instinct, especially at the end of the third. I was behind so badly that I was just trying to stay in it. I thought it was important that I never gave anything to her, she had to earn it to go in front."
Elsewhere, Maria Sakkari set up a second-round meeting with number one seed Elina Svitolina after a 6-3 6-3 win over Kristyna Pliskova, while Barbora Krejcikova beat Tereza Martincova 7-5 6-1.
Eighth seed Mertens came back from a break down in the deciding set to beat Alize Cornet 3-6 6-2 6-4.
Mertens, who had not beaten Cornet since 2018, will face either Petra Martic or Kamilla Rakhimova in the next round as she bids to reach her first quarter-final of 2022.
"It was a very tight match," Mertens said. "It could go either way, it was a battle. It's always difficult against her but I just kept fighting.
"I think I raised my level a little bit in the second and third sets. I stepped more into the court, the service was a bit better and I ran better."
Second seed Kontaveit needed three sets to get past Jil Teichmann, ultimately prevailing 6-3 1-6 6-3, while number five seed Belinda Bencic squeezed past Veronika Kudermetova 6-2 4-6 7-6 (7-5).
In Monday's other game, Ekaterina Alexandrova defeated Camila Giorgi 6-2 1-6 6-2.
Krejcikova had not won a singles title since her third triumph of 2021 in Prague last July, but ended her drought with a 6-2 6-3 defeat of the top seed.
The Czech ended the home favourite's hopes of being crowned champion in a showpiece match that was over in an hour and 21 minutes.
Kontaveit had won 24 consecutive indoor matches on hard courts, but she was no match for the 2021 French Open champion.
Krejcikova won 71 per cent of points on Kontaveit's second serve, breaking twice in the opening set and three times in the second.
She drew first blood to go 4-2 in the first following precise groundstrokes off both wings, then broke for a second time to seal an opening set in which Kontaveit made 13 unforced errors.
World number four Kontaveit responded with a break in the opening game of the second set, but failed to back that up with a hold.
Kontaveit had the initiative again at 3-1, but there was a sense of deja vu as her opponent broke straight back and served out the match after moving 5-3 in front with another break.
The world number four prevailed 0-6 6-4 7-6 (14-12) in a match that went the distance and will take on Paula Badosa, who beat in-form Daria Kasatkina in the other semi-final.
Krejcikova had lost five in a row against top-10 players and was soundly beaten in the first set, but she held in the second and earned the only break in the ninth game to level up.
That set up an incredible decider, which fourth seed Kontaveit led 6-5, but she could not take the first three of her match points as Krejcikova battled valiantly to force a tie-break.
Krejcikova felt her opponent's pain as she then squandered two match points of her own when leading 6-4.
It appeared neither player wanted to win as two more match points went begging for Krejcikova and four for Kontaveit in what turned into a real classic.
But Krejcikova eventually took her fifth opportunity to see off Kontaveit and reach a sixth WTA singles final.
"I think from both sides it was a really, really tough match," Krejcikova said. "I think we played wonderful tennis.
"It was very, very tight, and I'm really happy that I was able to hold the nerves better and that I won this match.
"I was just playing, just trying to fight for every single ball. When I had those match points down, I was just trying to figure out how to build up the point and how to win the point."
Badosa awaits Krejcikova in Saturday's final after beating Kasatkina in a match with far fewer twists and turns.
Competing in her second semi-final in as many weeks, it was similar disappointment for Kasatkina as she fell to a 6-2 6-2 loss.
French Open quarter-finalist Badosa hit 26 winners to Kasatkina's 12 and did not look back after winning 14 of the opening 16 points.
At the Adelaide International 2, meanwhile, it will be an all-American final as Madison Keys and Alison Riske advanced past Tamara Zidansek and Coco Gauff respectively.
Riske was given a walkover win against Zidansek, who withdrew with an abdominal injury, while Keys beat compatriot Gauff in three sets.
