Belinda Bencic got her grass-court season under way with a battling victory over qualifier Jule Niemeier in the first round of the inaugural bett1 Open.

Fifth seed Bencic came from a set down to beat 167th-ranked German Niemeier 4-6 6-4 7-5 in Berlin on Monday.

The 21-year-old Niemeier was playing her first professional match on grass and gave a great account of herself against the world number 12, who needed two hours and 12 minutes to secure her place in the second round.

Bencic secured the only breaks in the second and third set to ensure she will face Petra Martic or Asia Muhammad in round two.

Madison Keys progressed in straight sets, getting the better of Polish qualifier Magdalena Frech 6-3 6-4.

The American, a winner of two WTA singles titles on grass, struck 19 winners as she set up an encounter with top seed Aryna Sabalenka.

There were also first-round victories for Alize Cornet and Ekaterina Alexandrova earlier in the day over Amanda Anisimova and Anna Kalinskaya respectively.

Serena Williams said her serve was the key to battling past Mihaela Buzarnescu 6-3 5-7 6-1 in the second round of the French Open on Wednesday.

The win improved Williams' second-round record in grand slams to 74-2, her only defeats at this stage having come against sister Venus Williams when Serena made her major debut at the 1998 Australian Open, and against Garbine Muguruza seven years ago at Roland Garros in Paris.

Serena Williams won 75 per cent of the points played behind her first serve and saved five of the seven break points she faced in the French capital midweek.

"I felt it was pretty good today," Williams said of her serve. "But I've been practicing my serve a lot. I've been playing unbelievable on my serve in practice. The other night was, 'wow'. I'm glad it came better today.

"My coach told me it's good that I'm doing it well in practice because eventually it will be good in the match.

"I had some really good chances in the second set to win that. If I would have won just one point here or there, like four or five times, it would have been a different second set.

"I know going into the third I just had zero in on those one important points. If I could just take those, it would be an easier time for me."

The 39-year-old will continue her quest for a fourth Roland Garros title and record-equalling 24th slam crown against compatriot Danielle Collins, who beat Ukrainian qualifier Anhelina Kalinina 6-0 6-2.

"She's been playing well," Williams added. "She's also a really awesome person off the court. I love seeing her in the locker room.

"Ideally, it would be great if we didn't have to play each other because I always want her to do super well."

BENCIC DUMPED OUT BY KASATKINA

Belinda Bencic – the 10th seed – was dumped out by Daria Kasatkina 6-2 6-2, meaning there are no top-20 players left in the bottom quarter of the draw.

Bencic joined world number two Naomi Osaka, Bianca Andreescu and Kiki Bertens in departing the tournament after a dismal performance against Kasatkina, who will play in the third round of a major for the first time since Wimbledon in 2018.

Kasatkina's serve was in rude health, with the Russian and 2018 French Open quarter-finalist never facing a break point and racking up eight aces.

"A lot has changed between 2018 and now," said Kasatkina. "There was one amazing year for me, which was important in a good and in the bad way.

"I learned a lot, and I think I became a little bit different, maybe more experienced, a bit more serious. Let's say I understand more why I'm winning or why I'm losing.

"At that time everything was just going with the wave, and I was not thinking that much. Now I'm analysing more of what's going on in the situation I'm in. Getting maybe a bit more mature."

The only player left in that quarter who has previously reached a grand slam semi-final is 20th seed Marketa Vondrousova, who breezed past Harmony Tan 6-1 6-3. 

SABALENKA SEES OFF COMPATRIOT SASNOVICH

Third seed Aryna Sabalenka booked her spot in the third round with a 7-5 6-3 win over fellow Belarusian Aliaksandra Sasnovich, despite tallying 34 unforced errors.

Sabalenka, who has the second-most tour-level wins this season with 27, said: "I'm really proud of myself that I was fighting no matter what, kind of trying to find my rhythm. I'm really happy with this win. It was a tough battle.

"I would say I definitely feel better this year, kind of believe that I can do well here on the clay court. I feel better and really happy to be here, to compete here."

Sabalenka will now face 31st seed Anastasia Pavlyuchenkova in the next round after the Russian defeated Ajla Tomljanovic 6-2 6-3. 

There were also wins for two-time grand slam champion Victoria Azarenka, who overcame Clara Tauson 7-5 6-4, and Madison Keys, who beat Leylah Annie Fernandez 6-1 7-5.

Garbine Muguruza eased into the second round of the Internazionali BNL d'Italia on Tuesday thanks to a comfortable victory over lucky loser Patricia Maria Tig, though Belinda Bencic was the biggest casualty on a rain-interrupted day.

Spaniard Muguruza was due to face Anastasia Pavlyuchenkova until the Russian withdrew due to an abdominal issue, giving Tig a reprieve and the chance of an upset.

But Muguruza won all but three games in a comprehensive 6-1 6-2 victory that required little more than an hour on court as the former world number one went to 22-6 for the season.

Conditions were not great as drizzle persisted for much of the match, but Muguruza was grateful to progress after a generally testing day.

"It was a weird day," the 12th seed said afterwards. "I woke up [and the weather was] sunny, had an opponent. Then it turned out I had another opponent and it was raining the whole match. We had a little bit of everything!

"But, Rome, it's such a familiar tournament. I played here so many times, I've had nice matches. I love this clay, the red clay. It's familiar to me. I'm just looking forward to getting as many matches as possible."

Bencic will not be joining her in the next round, as she became the highest seed to be eliminated on the day in a 6-3 6-4 defeat to Kristina Mladenovic.

The two played each other under two weeks ago in the first round of the Madrid Open, with Bencic victorious, but Mladenovic got her revenge as she capitalised on her opponent's seven double faults.

Like Tig, Sloane Stephens was also competing as a lucky loser as she came up against compatriot Madison Keys, though the outcome was no different.

Keys claimed only her second win in six meetings with Stephens but had to come from behind as she eventually clinched it 4-6 6-2 7-5 after two-and-a-half hours on court to set up a clash with 15th seed Iga Swiatek.

Elise Mertens, the 14th seed, was also dumped out of the competition, losing out 4-6 6-2 6-3 to Veronika Kudermetova, whom she had beaten in straight sets in their three WTA Tour contests before this one.

Veteran Kazakh Yaroslava Shvedova, ranked 665 in the world, awaits top seed Ashleigh Barty after the 33-year-old showed character to fight back and beat Martina Trevisan 0-6 7-6 (7-4) 7-6 (8-6), while Nadia Podoroska set up a second-round clash with Serena Williams after seeing off Laura Siegemund 2-6 7-6 (7-3) 6-1.

Ash Barty won her first match on clay since reigning supreme at the 2019 French Open as the world number one rolled into the Volvo Car Open round of 16.

Barty – who last featured in a clay-court match en route to Roland Garros glory almost two years ago amid the coronavirus pandemic – made light work of Misaki Doi 6-2 6-1.

Miami Open champion last week, top seed Barty continued where she left off at the WTA 500 event on Wednesday, closing out proceedings in just over an hour in Charleston.

"I had to use it as an opportunity to try and build some comfort," Barty said. "I think having a couple days between Miami and playing this first match was important, to have my body rest, but to also try and prepare to change surfaces. It was a very quick turnaround, but I felt great out there tonight."

Barty – who now boasts a 15-2 win-loss record in 2021 – will next face Shelby Rogers after she outlasted 13th seed Amanda Anisimova 1-6 7-5 6-4.

As for second seed Sofia Kenin, the 2020 Australian Open champion slumped to a shock 4-6 6-3 6-4 defeat against Lauren Davis midweek.

World number four Kenin – runner-up at last year's French Open – eased to the first set but fellow American Davis, ranked 79th in the world, changed tactics to fine effect.

"I was a bit uncomfortable so I just really dug deep and really started to think about how to beat her and I found that heavy deep balls were not her favourite," the 27-year-old Davis said.

"Being on clay, the ball bounces high, pushing girls back, so it's very effective."

Kenin took a medical timeout at 3-0 down in the deciding set but, despite reeling off the next three games, she was unable to see Davis off as her 2021 woes continue.

Davis now heads into another all-American clash with teenage sensation Coco Gauff – who came from 1-3 down in the third to defeat Liudmila Samsonova 4-6 6-1 6-4 in an absorbing two-hour contest.

Belinda Bencic – the fifth seed – crashed out as Paula Badosa claimed the first top-20 win of her career following a 6-2 6-7 (2-7) 6-1 success.

Badosa will face Caty McNally in the last 16 after the 19-year-old American beat Anastasija Sevastova 7-6 (7-3) 2-6 6-4.

Seventh seed Elise Mertens was another big name to depart as Alize Cornet prevailed 7-5 6-3, although 15th seed Veronika Kudermetova and 12th seed Ons Jabeur progressed in with the minimum of fuss.

Former US Open champion Sloane Stephens, meanwhile, topped eighth seed Madison Keys 6-4 6-4.

Seeds were even more vulnerable at the Copa Colsanitas in Bogata, including the top-seeded Saisai Zheng who was dispatched 6-4 6-1 by Stefanie Voegele.

Zheng's compatriot Yafan Wang, seeded eighth, went down 6-3 6-3 to Viktoriya Tomova.

Arantxa Rus and Jasmine Paolini, the third and sixth seeds respectively, lost in three to Spanish duo Nuria Parrizas Diaz and Lara Arruabarrena.

Madison Keys is intent on giving Maria Sakkari a second-round test after marking her first WTA Tour appearance since September with a clinical win at the Qatar Open.

American world number 19 Keys, who reached the US Open final in 2017, had not played on tour since losing to Zhang Shuai in the first round of the French Open in late September – she was ruled out of the Australian swing of this season after a positive coronavirus test.

But Keys roared back to action with a thumping 6-4 6-1 victory over Belinda Bencic on Tuesday, the Swiss who last week reached the Adelaide International final.

"I'm really happy with how I came out and played today," Keys said. "I'm a little bit surprised with myself but hoping to keep the momentum going."

Sakkari promises to pose a tricky test for Keys, who is unseeded this week, given the Greek player dropped only three games in her opening win over Mayar Sherif and has shown bright early-season form.

World number 23 Elena Rybakina tripped up in the first round after the Moscow-born Kazakh player lost 7-6 (9-7) 7-6 (7-5) to Germany's 56th-ranked Laura Siegemund at the WTA Premier event.

Jessie Pegula, Anastasia Pavlyuchenkova, Ons Jabeur and Misaki Doi also scored straight-sets victories in Doha.

At the Lyon Open, French players Caroline Garcia and Kristina Mladenovic were both pushed to three sets before inking their places in the last 16.

Third seed Garcia edged compatriot Oceane Dodin 6-2 2-6 6-3, while fourth seed Mladenovic scrambled for a 5-7 7-5 6-2 win over Romanian Mihaela Buzarnescu.

Former Wimbledon runner-up Eugenie Bouchard, in on a wildcard, was bounced out 7-6 (9-7) 6-2 by Aliaksandra Sasnovich, the world number 96 from Belarus.

Madison Keys is set to miss the Australian Open after testing positive for coronavirus.

The 2017 US Open runner-up announced on Thursday that she contracted COVID-19 before she was due to fly out for the first grand slam of the year.

Keys did not state she will definitely miss the major, which starts on February 8, but it appears the American will not make the trip to Melbourne.

The American wrote on Instagram: "Hi everyone, I wanted to let you know that I unfortunately tested positive for COVID-19 before I was supposed to fly to Australia.

"I'm very disappointed to not be able to play in the coming weeks after training hard in the off-season and knowing Tennis Australia and the tours did so much to make these events happen.

"I am self-isolating at home and will continue to follow all the necessary health precautions. I look forward to being back on tour next month."

It was revealed earlier in the day that three-time major winner Andy Murray has also tested positive for the virus, but still hopes to play in the Australian Open.

Meanwhile, world number 50 Tennys Sandgren was cleared to board a flight from the United States bound for Melbourne despite revealing he returned a new positive coronavirus test this week. 

The American, twice a quarter-finalist at Melbourne Park, initially posted to social media on Wednesday that he had tested positive for the virus for a second time. 

Although his first instance of having the illness was recorded in November, the 29-year-old's participation in the tournament appeared to be in doubt. 

But as he continued to update followers through the day, it emerged he had been allowed to board his flight. 

Players will only be allowed into Australia with proof of a negative test just prior to departure, or with approval to travel as a recovered case at the complete discretion of an Australian government authority.

Anyone wanting to travel out for the tournament who previously tested positive is required to provide additional and highly detailed medical information as proof they are a recovered case and no longer infectious or a risk to the community.