Naomi Osaka suffered a shock second-round exit to Karolina Muchova at the Madrid Open, but there was no such trouble for Simona Halep as she held off Zheng Saisai.

Second seed Osaka was playing just her second match on clay since the 2019 French Open due to injury issues and became the latest big name to fall at the hands of Muchova.

The world number 20, who had already defeated two top-five players this season, prevailed 6-4 3-6 6-1 in a time of one hour and 49 minutes in the Spanish capital.

Osaka has now lost two of her last three matches, having been eliminated from the Miami Open quarter-finals by Maria Sakkari at the end of March.

"I think today for me it was quite different from the last time I lost in Miami, and I actually think I played much better here, so I'm very happy about that," Osaka said.

"I think what I can take away from this is that I tried my best throughout the entire match. I think tennis-wise, I felt I was too defensive in the first set.

"I wouldn't say I’m happy that I lost, but I think I learned a lot. So that's all I can hope for."

Two-time champion Halep has yet to drop a set in this year's tournament after seeing off unseeded opponent Zheng 6-0 6-4.

Halep took nine games in a row at the start of the match but, like in her opening-round win over Sara Sorribes Tormo, she had to hold off a late surge from her opponent to advance.

Next up for Halep is a last-16 showdown with Elise Mertens, who beat Elena Rybakina 7-6 (7-4) 7-5 in the last of Sunday's matches.

Fifth seed Aryna Sabalenka safely advanced earlier in the day thanks to a 6-3 6-3 win against Daria Kasatkina, while Sakkari beat Anett Kontaveit 6-3 6-1.

Sabalenka was on course to face Victoria Azarenka for a place in the quarter-finals, but the Belarussian withdrew from her match with Jessica Pegula because of a back injury.

Elsewhere, Jennifer Brady, who knocked out fellow American Venus Williams in the first round, eased past Jelena Ostapenko 6-2 6-1.

Brady faces a tricky test in the next round with Anastasia Pavlyuchenkova, who defeated sixth seed Karolina Pliskova 6-0 7-5, seeking another scalp.

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.

Eighth seed Ann Li toppled the top remaining seed Zheng Saisai in the quarter-finals of the Monterrey Open on Friday, throwing the field wide open.

Li triumphed 7-5 6-1 over third seed Zheng, who held the highest rank of all remaining players after Sloane Stephens and Nadia Podoroska's first-round exits.

World number 52 Zheng struggled to win on her first serve, with Li converted five of seven break points.

American Li, who is ranked 72nd in the world, will next face Swiss qualifier Viktorija Golubic, who beat Russia's Anna Kalinskaya 6-2 6-4.

On the other side of the draw, Canadian Leylah Fernandez defeated Slovakia's Viktoria Kuzmova 7-5 6-3 and will face seventh seed Sara Sorribes Tormo in the other semi-final.

Sorribes Tormo, who is now the highest ranked remaining player, defeated Anna Karolina Schmiedlova 6-3 7-5.

Third seed Zheng Saisai comfortably accounted for countrywoman Zhu Lin to reach the quarter-finals of the Monterrey Open on Thursday.

Zheng, who is ranked 27th in the world, triumphed 6-1 6-2 in a dominant display where she was seldom challenged.

In the last eight, Zheng will face eighth seed Ann Li, who overcame Slovenian Tamara Zidansek 6-4 6-3 at the WTA International tournament.

Zheng is the highest remaining seed left standing in the draw after the first-round exits of top seed Sloane Stephens and Nadia Podoroska.

Russian qualifier Anna Kalinskaya continued her good run with a 6-4 6-3 victory over Nina Stojanovic and she will next face Viktorija Golubic in the quarters – the latter topped Lauren Davis 6-3 6-1.

Danielle Rose Collins will face world number one Ash Barty after beating Zheng Saisai at the WTA Adelaide International.

The American wrapped up a 7-6 (7-5) 6-1 victory and will now face top seed Barty, who will still be smarting from her surprise quarter-final exit at the Australian Open.

Barty is the reigning champion in Adelaide and will be seeking to put that loss to Karolina Muchova firmly behind her.

Collins' compatriot Shelby Rogers also prevailed, beating Veronika Kudermetova 6-3 7-6 (7-4) to set up a clash with third seed Johanna Konta.

Anastasija Sevastova overcame Caroline Garcia 6-2 6-4, while eighth seed Wang Qiang was a 6-4 6-3 winner over teenager Olivia Gadecki.