Kudermetova had won her only two previous singles matches against Kontaveit and maintained that perfect record with a 7-5 6-1 victory.
The world number 46 from Russia broke four times to seal her place in the second round, with Kontaveit winning just 48.4 per cent of points on her first serve in a rusty beginning to the 2021 campaign.
Donna Vekic was another seed to fall at the first hurdle as Bernarda Pera consigned the Croatian to a 7-6 (12-10) 2-6 6-4 defeat at Zayed Sports City International Tennis Centre.
Kirsten Flipkens could face top seed Sofia Kenin in the second round after defeating Laura Siegemund 5-7 7-5 6-4.
Ons Jabeur is aiming to break into the top 10 this year and the 15th seed got up and running for the season by seeing off Anastasia Pavlyuchenkova 7-6 (7-3) 6-3.
Daria Kasatkina, Yulia Putintseva and Ajla Tomljanovic were among the other players who advanced to round two.
Kvitova – who won the 2018 and 2021 editions of the tournament, beating Garbine Muguruza in the final on both occasions – was left unable to continue during her clash with Elise Mertens, later tweeting that an injury to her left wrist had flared up during the second set.
Her conqueror Mertens will face fourth seed and WTA St Petersburg champion Anett Kontaveit in the round of 16 after the Estonian's win over Ana Konjuh on Monday.
Meanwhile, Azarenka joined Kvitova in announcing her withdrawal through injury, suffering pain in her left hip ahead of her scheduled clash with American Madison Brengle.
The tournament's top seeds had more luck on a day of few surprises. World number two Aryna Sabalenka breezed to a 6-2 6-2 victory over France's Alize Cornet, with the Belarusian the favourite for the first WTA 1000 event of the year as world number one Ashleigh Barty is missing through injury.
Elsewhere, world number three Barbora Krejcikova made light work of Poland's Magda Linette, winning 6-1 6-3, and will face former French Open champion Jelena Ostapenko in the round of 16, having eliminated the Latvian from last month's Australian Open.
Paula Badosa also recorded a straight-sets victory, seeing off Clara Tauson 6-1 6-2 to reach the last 16, where she will face 17-year-old American Cori Gauff, who defeated France's Caroline Garcia 6-2 7-6 (7-3).
There were also three-set wins for top-10 players Iga Swiatek and Ons Jabeur, with Swiatek beating Viktorija Golubic 6-2 3-6 6-2, and Jabeur overcoming Aliaksandra Sasnovich 1-6 7-5 6-3.
In the final match of the day, world number six Maria Sakkari downed American Ann Li 6-3 6-3.
Two-time Wimbledon champion Kvitova lost to Aryna Sabalenka in the 2020 final but has looked on top form throughout the week in Doha.
Kontaveit proved a tough opponent for the fourth seed, however, and Kvitova – the 2018 champion – needed three sets to progress 6-3 3-6 6-2.
"I'm really glad that after losing the second set, which I probably didn't play the best, I started very well in the third," said Kvitova.
"I learned that the return was pretty good from my side. I was going for it – first point, first shot – and I think that made a big difference. In the rally, it was 50-50 and anybody could win it, but when I put the pressure from my return, it was really very nice."
Her reward is a semi-final tie with qualifier Jessica Pegula, who caused an upset by defeating second seed Karolina Pliskova 6-3 6-1.
Pegula reached the Australian Open quarter-finals last month and played with supreme confidence to oust the 2017 champion and reach her maiden semi-final at a WTA 500 event.
The other half of the draw will see Victoria Azarenka taking on Garbine Muguruza.
Azarenka triumphed 6-2 6-4 over top seed Elina Svitolina, with the two-time Doha champion maintaining her unbeaten record against the Ukrainian to reach the 60th WTA semi-final of her career.
Muguruza, meanwhile, battled past Maria Sakkari 6-3 6-1 to complete the last four.
At the Lyon Open, French duo Kristina Mladenovic and Clara Burel booked their places in the last eight, beating Margarita Gasparyan and Aliaksandra Sasnovich respectively.
Spaniard Paula Badosa awaits Mladenovic, while teenage wildcard Burel takes on compatriot and second seed Fiona Ferro in what is her first WTA quarter-final.
There were also victories for Greet Minnen and Viktorija Golubic.
Martic – the tournament's top seed – triumphed 6-0 6-3 in just over an hour as she played for the first time since February, the WTA Tour having been suspended amid the coronavirus pandemic.
The clay-court event in Italy has seen action resume on the Tour, though world number two Simona Halep withdrew before the event started due to travel concerns.
Her absence is a boost for Martic's hopes of success, with the Croatian showing few signs of rustiness against Van Uytvanck.
"I think I felt my nerves a little bit more, because the break was so long," Martic told media via video chat.
"It's such a big uncertainty going on the court not knowing how you're going to be.
"I played well before the break, so I was happy with the rhythm, but obviously five months off disrupts everything. Once the match started, I kind of let go and just played."
Anett Kontaveit also progressed in straight sets, the fourth seed winning the final six games to record a 6-3 6-3 victory over Patricia Maria Tig in a late finish.
However, there were some big-name casualties on Tuesday.
Marketa Vondrousova won the opening set with ease, yet the second seed slipped up after such an impressive start, serving up double faults during her 1-6 7-5 6-4 defeat to Kaja Juvan.
Elise Mertens, the fifth seed, is also out. The Belgian went down 6-4 6-1 to Aliaksandra Sasnovich.
Martic, the top seed at the WTA International event that marks the return of the Tour amid the coronavirus pandemic, overcame Liudmila Samsonova 5-7 6-4 6-2.
Croatian Martic, the world number 15, needed two and a half hours to get past the qualifier in Italy on Thursday.
She will face Aliaksandra Sasnovich in the last eight.
Kontaveit was also pushed before recording a 3-6 6-2 6-2 victory over Laura Siegemund.
Yastremska and Camila Giorgi will meet in a quarter-final after respective wins over Oceane Dodin and Kaja Juvan.
Talented Ukrainian seventh seed Yastremska was too good for Dodin 6-2 6-4, while Giorgi beat Juvan 3-6 6-2 6-4.
Top seed Martic battled past qualifier Aliaksandra Sasnovich 7-6 (7-5) 7-6 (7-3) in their quarter-final.
The Croatian converted four of seven break points and saved seven of 11 to advance at the WTA International event, which marks the first tournament back after the coronavirus-enforced break.
Martic will meet Kontaveit, who beat teenage wildcard Elisabetta Cocciaretto 6-1 4-6 6-1.
Unseeded pair Camila Giorgi and Fiona Ferro will meet in the other semi-final.
Giorgi got past seventh seed Dayana Yastremska 4-6 7-6 (7-5) 6-3 after saving two match points, while Ferro brushed past Italian veteran Sara Errani 6-4 6-1.
Muguruza, the Spanish sixth seed at the WTA 500 event, crushed Marketa Vondrousova 6-1 6-0 on Saturday.
The two-time grand slam champion has lost just 10 games in four matches on her way to the final.
Muguruza lost just eight points on serve against Vondrousova while converting five of 11 break points.
She will meet Barty in the final after the Australian benefited from Serena Williams' withdrawal as the 23-time grand slam winner deals with a shoulder injury.
Naomi Osaka and Victoria Azarenka also withdrew on Saturday from the Gippsland Trophy and Grampians Trophy respectively.
At the Grampians Trophy, Anett Kontaveit was given a passage into the semi-finals, where Maria Sakkari awaits after her 6-4 6-2 win over Angelique Kerber.
Jennifer Brady and Ann Li will meet in the other semi after wins over Barbora Krejcikova and Sorana Cirstea respectively.
Elise Mertens will play the Gippsland Trophy final after Osaka's withdrawal with the Belgian to face Kaia Kanepi, who overcame Ekaterina Alexandrova 6-3 7-6 (8-6) to reach her first WTA decider since 2013.
Estonian Kontaveit, ranked 30th in the world, claimed her fourth top-20 win of the season as she prevailed 6-4 6-3 on Friday.
Kontaveit also defeated Bencic in the 2020 Australian Open, meaning she is 2-0 in their head-to-head rivalry.
Czech left-hander Kvitova awaits in the last four, after the second seed defeated Bencic's Swiss compatriot Jil Teichmann 6-4 6-4.
Teichmann beat Kvitova in their only previous meeting, but the world number 10 had too much on this occasion, along with the backing of the crowd to boot as she chases a 29th singles title of her career.
The other semi-final will see top seed Iga Swiatek face Maria Sakkari.
Last year's French Open winner Swiatek reached her first semi-final since May – when she landed the prestigious title in Rome – by overcoming Elena Rybakina 7-6 (7-5) 6-2.
Sakkari, meanwhile, ended Tereza Martincova's hopes in straight sets.
Greek star Sakkari ended Swiatek's reign as Roland Garros champion in June, beating the Polish 20-year-old in the quarter-finals in Paris.
Japanese star Osaka rallied past Kontaveit in three sets at the WTA Premier tournament in New York, where the event is being held instead of Cincinnati amid the coronavirus pandemic.
Sakkari, who conquered 23-time grand slam champion, Serena Williams, in the last 16, bowed out in the quarter-finals on Wednesday.
OSAKA OUTLASTS KONTAVEIT
Two-time grand slam champion Osaka was made to work for her 4-6 6-2 7-5 victory over 12th seed Kontaveit.
After dropping the opening set, fourth seed Osaka regrouped – reeling off nine successive games and hitting 29 winners to earn a semi-final showdown against Elise Mertens.
It is Osaka's second semi-final of the year following her final-four run at the Brisbane International prior to January's Australian Open.
Mertens – the 14th seed – awaits following her routine 6-1 6-3 victory over American qualifier Jessica Pegula.
SAKKARI SENT PACKING
After claiming the scalps of Coco Gauff and former world number one Williams, 13th seed Sakkari suffered a 6-4 6-3 loss to Johanna Konta.
Sakkari was unable to continue her fine run ahead of the US Open as British eighth seed Konta reached her second Premier semi-final thanks to 18 winners, four aces and three breaks of serve.
AZARENKA ROLLS ON
A two-time Australian Open champion, Victoria Azarenka is next up for Konta after the 2013 Cincinnati winner edged Ons Jabeur 7-6 (11-9) 6-2.
Azarenka emerged victorious in one hour, 44 minutes as the resurgent Belarusian moved into the Western & Southern Open semis for the first time in seven years.
Osaka won the first three games of the match to jump out to an early lead, securing the set with a double-break before breaking early in the second to cruise to a 6-2 6-3 win.
The story of the match was Osaka's ease in winning points against Kerber's serve, winning 41 per cent (15/37) of Kerber's successful first serves, while the German could only win 11 per cent (3/27) in the same category.
Britain's top-ranked woman Emma Raducanu suffered another early exit, on the wrong end of Katerina Siniakova's comeback 3-6 6-4 7-5 win.
Ostapenko, looking to add to the fifth career title she won in Dubai 12 months ago, edged an entertaining contest 7-5 1-6 7-5 in two hours and 19 minutes.
Fellow seeded player Anett Kontaveit was also victorious on the opening day of the tournament, but only after battling back to beat Zhang Shuai 4-6 7-6 (7-4) 6-4.
Marta Kostyuk saw off Sorana Cirstea 6-2 1-6 6-2, meanwhile, and will now face second seed Belinda Bencic in the next round.
Elise Mertens is also through to round two, where Veronika Kudermetova awaits, after dominating Martina Trevisan 6-0 6-2.
In the first main draw match at the Linz Open, Sofia Kenin let an early lead slip to lose 2-6 6-3 6-4 to Jule Niemeier.
The Latvian was the first wildcard to reach the final since Daniela Hantuchova in 2000 and kept up her good form ahead of Wimbledon by beating Kontaveit 6-3 6-3.
French Open 2017 winner Ostapenko dominated from the start and picked up the victory in one hour and five minutes, adding to her three previous career WTA titles.
She has now won titles on all four surfaces – clay, hard, indoor and grass – and is hopeful of improving on her current ranking of 43rd in the world.
"I think it says that I can be dangerous and playing well on all surfaces probably," she said in her on-court interview.
"Of course I enjoy to play more on just some of them, but in general I can adjust well to different surfaces.
"I think this is just the beginning for me. If I keep playing the way I played this tournament, I think I can be back in top 10 and play well.
"I just have to keep that in my mind and work even harder."
Ostapenko made good use of her strong service game to break Kontaveit's serve in the third and fifth games.
Kontaveit earned a first break in the eighth game with four service return winners in a row, but Ostapenko recovered from 40-15 in the next game to take the opening set.
It was then plain sailing for Ostapenko in the second set as she earned the only break at 2-1 and held for the remainder, clinching the victory with her second championship point.
Ostapenko will face Leylah Fernandez in the first round of Wimbledon next week.
The world number 81 continued her rich vein of form, having also captured the Budapest Grand Prix crown last weekend.
Pera, who won four out of six break points, stretched her winning streak to 12 matches, while she has also now reeled off 24 sets without reply.
Kontaveit had prevailed as a commanding straight-sets winner when the pair faced off in the opening round at Wimbledon four weeks ago.
Champion in St Petersburg and runner-up to Iga Swiatek in Doha, the Estonian became the fourth player to appear in at least three finals this season after Swiatek, Ons Jabeur and Veronika Kudermetova.
But the top seed was broken in the opening game by Pera, who won 16 out of 19 points on her first serve as she stormed through the first set.
The American then rescued two break points in the second set, while converting two of her own to secure consecutive breaks and move to the brink of the title.
Kontaveit dug deep; breaking back and winning eight of the next 11 points to stay alive at 5-4, but a long forehand in the next game sealed the deal for Pera.
Putintseva was the strong favourite to overcome world number 86 Parry, but it was the latter who prevailed 6-3 6-4 to reach her first tour-level quarter-final.
Caroline Garcia also advanced through after recovering from a heavy first-set loss to overcome Elisabetta Cocciaretto 0-6 6-3 6-4.
Home hope Lucia Bronzetti awaits in the final eight following a 6-1 6-3 win over Elina Avanesyan, while Nuria Parrizas-Diaz beat Julia Grabher 6-2 6-4 in the day's other match.
At the Hamburg European Open, in-form Bernarda Pera beat Katerina Siniakova 6-3 6-1 to make it 10 wins in a row without dropping a set.
Pera is through to her second semi-final in a row, where she will take on Maryna Zanevska, who saw off Aliaksandra Sasnovich in straight sets for a second career top-50 victory.
Top seed Anett Kontaveit advanced after Andrea Petkovic withdrew injured when 6-0 2-0 down, but Barbora Krejcikova was on the end of a 6-1 6-3 upset against Anastasia Potapova.
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 celebrated her first WTA Tour win at the expense of Polona Hercog in Cluj on Tuesday and followed that up with a 6-3 6-4 defeat of Ana Bogdan.
The 18-year-old US Open champion had a first-serve percentage of 69 and won 87 per cent of those points, breaking three times to move into the last eight.
Third seed Raducanu said: "It's definitely taking me some time to find my feet still. I'm just taking some learnings from every match that I play. I don't think I'm the finished product yet."
Next up for the Brit is a meeting with fellow teenager Marta Kostyuk after the sixth seed sent Mona Barthel packing with a 6-4 6-4 victory.
Halep was troubled by a back injury in a 6-4 6-2 success over Varvara Gracheva in her homeland.
The two-time grand slam champion played through the pain barrier, breaking twice in each set to progress, and could face Raducanu if she beats fellow Romanian Jaqueline Cristian.
"The back got blocked and the pain is really big," Halep said in the on-court interview. "You cannot really bend much and you cannot move.
"But sometimes you are used to the pain, I had this before many times, and I just wanted to continue and finish this match. It's good that I won this match, I don't know how."
Anett Kontaveit, striving to secure a WTA Finals berth, extended her indoor winning run to 12 matches by seeing off Alison Van Uytvanck 6-3 6-4, while Rebecca Peterson knocked Irina Bara out in straight sets.
In the Courmayeur Open, Jasmine Paolini came out on top 6-4 7-5 in an all-Italian battle with Lucrezia Stefanini and Zhang Shuai got past Wang Xinyu 7-6 (7-5) 6-4.
The unseeded Donna Vekic also secured a place in the quarter-finals.
US Open champion Raducanu claimed her first ever regular WTA Tour win in Cluj earlier this week, with the 18-year-old keen to impress in the homeland of her father, but Kostyuk denied her the chance of a dream last-four clash with Halep.
The 19-year-old Ukrainian swept Raducanu aside in just 57 minutes, winning 6-2 6-1 as Kostyuk furthered her own burgeoning reputation in the game by reaching a third semi-final of the year.
Raducanu proved her own worst enemy, her 41 unforced errors more than double Kostyuk's 16, with the latter feeling confident as early as the first game when two double faults helped her break the Briton's serve.
"I don't know how I won the first game, I think that's where everything started," Kostyuk said. "I somehow won that game and I gained this confidence, like I'm not going to lose this match.
"After that, by the fifth game maybe, I figured out how to play her – today. Maybe next time I play it's going to be different tactics."
Top seed Halep enjoyed a similarly straightforward victory as she lost just two games en route to a 6-1 6-1 win over Romanian compatriot Jaqueline Cristian, a particularly impressive feat given she had been suffering with a back injury this week.
That success preserved Halep's 100 per cent record against fellow Romanians.
On the other side of the draw, second seed Anett Kontaveit was also an impressive winner as she disposed of Anhelina Kalinina 6-1 6-3 in just over an hour. Kontaveit has won 24 of her last 26 matches and will be the firm favourite against unseeded Rebecca Peterson, who beat Lesia Tsurenko 6-2 3-6 6-3.
At the Courmayeur Open in Italy, third seed Liudmila Samsonova cruised into the semis thanks to a swift 6-1 6-2 demolition of Anna Kalinskaya. She will meet Clara Tauson – seeded fifth – after the Dane came through a more gruelling 3-6 6-4 6-2 win over Ann Li.
The other semi will be contested by Donna Vekic and Jasmine Paolini, who were straight-sets winners over Wang Xinyu and Dayana Yastremska, respectively.
Kontaveit went into Sunday's final knowing victory over top seed Halep would earn her the last place in the season-ending tournament in Guadalajara.
The Estonian duly denied Ons Jabeur a WTA Finals spot, beating Romanian home favourite Halep 6-2 6-3 in Cluj.
Second seed Kontaveit has now come out on top in 10 consecutive matches, having won the Kremlin Cup last weekend, and this was her fourth title of a stellar season.
Halep had not dropped a set in her previous three meetings with Kontaveit, but the former world number one was soundly beaten to miss out on a fourth title on home soil – five years after her last in Bucharest.
The 25-year-old Kontaveit took her run to 26 victories in her last 28 matches, winning 70.6 per cent of points behind her first serve to Halep's 44.1 per cent.
Kontaveit broke three times in a one-sided first set and fought back from 2-0 down in the second to continue her brilliant run.
Halep has not won a title since September 2020, having been unfortunate with injuries this year.
Ninth seed Kontaveit ousted Vondrousova in Moscow on Saturday with a commanding 6-3 6-4 victory.
The Estonian had lost both of her previous two meetings with Vondrousova, but needed only an hour and 14 minutes to reach her fifth final this year.
Kontaveit struck 26 winners, with her backhand a potent weapon, and broke five times – three of those coming in the first set after she failed to hold in the first game of the match.
The 25-year-old Tallinn native has lost only two of her past 22 matches, while her winning run indoors now stands at nine.
Standing in the way of Kontaveit and a fourth title in 2021 is home hope Alexandrova, who advanced to her first WTA 500 final when Maria Sakkari retired due to dizziness.
Alexandrova was leading 4-1 in the opening set when the fourth seed from Greece decided she was unable to continue.
There will be an unseeded champion at the Tenerife Open after Colombian Camila Osorio beat Camila Giorgi 6-4 7-5.
Ann Li will play in her second title-decider of the year courtesy of an emphatic 6-2 6-1 triumph over Alize Cornet.
Top seed Sakkari faced Ekaterina Alexandrova in the second round and recorded a routine 6-2 6-4 triumph as she looks to bounce back from a fourth-round exit at the Australian Open.
The Greek will next face a difficult contest with Elise Mertens, who needed three sets to see off the challenge presented by Petra Martic and seal a 6-4 3-6 6-2 success.
Second seed Kontaveit recorded a 6-4 7-5 victory over Romania's Sorana Cirstea to set up a tantalising meeting with Belinda Bencic after the Swiss downed Kaja Juvan 6-1 7-6 (7-2).
World number 12 Elena Rybakina, meanwhile, needed less than an hour to record a straight-sets victory over Varvara Gracheva, booking an encounter with Tereza Martincova in the round of 16.
