Second seed Naomi Osaka picked up where she left off at last month's Australian Open, winning her first match since lifting the title in Melbourne.

Osaka earned her place in the Miami Open third round on Friday with a hard-fought straight-sets victory over Australian Ajla Tomljanovic.

Australian Open runner-up Jennifer Brady was knocked out in the second round by 58th-ranked Sara Sorribes Tormo.

Brady's defeat was the major surprise on Friday, with Sorribes Tormo fighting back from a set down to win.

Top 10 seeds Karolina Pliskova, Bianca Andreescu and Sofia Kenin also progressed, with the latter coming from a set behind to beat Andrea Petkovic.

OSAKA CONTINUES WINNING RUN

Osaka extended her winning streak to 22 matches, although it was not easy against Tomljanovic.

The Japanese got the edge 7-6 (7-3) 6-4, firing down 36 winners, including 13 aces in a match lasting one hour, 38 minutes.

"This is my first match since Australia, so I just really wanted to play well," Osaka said in her on-court post-match interview. "I kind of feel like I'm at home here, because I grew up [near here] for most of my life."

Tomljanovic did not go down without a fight but was let down by 24 unforced errors.

Osaka will next face Serbian qualifier Nina Stojanovic in the third round.

BRADY BEATEN AGAIN

World number 14 Brady succumbed to in-form Monterrey Open semi-finalist Sorribes Tormo 3-6 6-4 6-1.

Brady had a dream run to the final at the Australian Open last month but came back to earth with a thud against the Spaniard, who has won 10 of her past 11 matches.

The match lasted two hours, 22 minutes, with Sorribes Tormo finding the edge in the last as Brady's first-serve percentage dropped to 30.8 per cent.

Brady's defeat comes a few weeks after being humbled by Anett Kontaveit in less than an hour in the Qatar Open first round.

MIXED BAG FOR SEEDS

Tenth seed Kiki Bertens, in her third match back from Achilles surgery, was knocked out by Russian qualifier Ludmilla Samsonova 6-2 6-1 inside an hour.

Fourth seed and last year's Australian Open champion Kenin responded after losing the first set to defeat Andrea Petkovic, winning 6-7 (6-8) 6-1 6-3. The match was Kenin's first since appendix surgery.

Sixth seed Pliskova comfortably got past Zheng Saisai 6-2 6-1 and 2019 US Open champion Andreescu triumphed over Tereza Martincova 7-6 (7-5) 6-2.

Seeds Elena Rybakina, Kontaveit, Maria Sakkari, Ons Jabeur and Amanda Anisimova all won, with 20th seed Petra Martic and Sloane Stephens both knocked out.

Ash Barty completed a great escape to stay alive at the Miami Open, where Simona Halep also progressed.

Barty faced a match point but the defending champion and world number one dug deep to prevail in three sets against Kristina Kucova on Thursday.

Romanian third seed Halep also needed three sets at the WTA Premier tournament in Miami.

BARTY PRODUCES COMEBACK

In her first match outside of Australia in more than 12 months, Barty survived to top qualifier Kucova in Miami.

Barty trailed 5-2 in the third set, with Kucova earning a match point at 5-3 but the Australian star saved it and won the final five games of the match to secure a spot in the round of 32.

Winner of the 2019 French Open, Barty sent down an equal career-high 15 aces in two-and-a-half hours.

"Today was really hard work, and I enjoyed every single minute of it," Barty said on court post-game. "There’s nothing like coming through a test like that, and now I get another opportunity in a couple days' time to play another tough match and test myself again."

Next up for Barty is 2017 Roland Garros champion Jelena Ostapenko, who outlasted Kirsten Flipkens 6-2 5-7 6-3.

HALEP REACHES MILESTONE

Halep brought up her 400th WTA main-draw triumph with a 3-6 6-4 6-0 victory over France's Caroline Garcia.

After dropping the opening set, Halep won 11 of the final 12 games to move through to the next round.

Halep won in one hour, 48 minutes, drastically improving on her first serve after the opening set while coming to grips with Garcia's kick serve.

"I needed time to get used to it and to get the rhythm," Halep said about Garcia's serve having improved her head-to-head record to 7-1, with Anastasija Sevastova awaiting in the last 32 after eliminating American sensation Coco Gauff.

Halep received attention on her shoulder early in the second. "I struggled with my serve," Halep said. "I struggled with my shoulder a little bit, so the attention was a little bit on the pain. [After that] I started to relax myself."

KERBER'S DOUBLE BAGEL

Three-time grand slam winner Angelique Kerber has been up and down in recently, but she flexed her muscles with a 6-0 6-0 humiliation of Renata Zarazua.

Aryna Sabalenka – the seventh seed – was another one to fend off match points before rallying 0-6 6-3 7-6 (11-9) past Bulgarian qualifier Tsvetana Pironkova in a gutsy.

Last year's French Open champion Iga Swiatek knocked off Barbora Krejcikova 6-4 6-2, while ninth seed and two-time Wimbledon champion Petra Kvitova got past Aliza Cornet 6-0 6-4.

Fifth seed Elina Svitolina survived to beat Shelby Rogers 3-6 7-5 6-3 and two-time major winner Victoria Azarenka benefited from a walkover.

Sloane Stephens ended her losing run to start the year with a hard-fought three-set win over France's Oceane Dodin in the first round of the Miami Open on Wednesday.

Former US Open champion Stephens, ranked 49th in the world, defeated Dodin 6-7 (6-8) 6-4 6-2.

Stephens progresses to the second round where the top seeds, including top three Ash Barty, Naomi Osaka and Simona Halep, will be introduced and she will face 28th seed Amanda Anisimova.

Danielle Collins, Wang Qiang, Alize Cornet and Caroline Garcia were among the other winners on Wednesday, while Svetlana Kuznetsova bowed out.

SLOANE FIGHTBACK

Stephens had endured a dismal start to 2021, enduring an 0-4 win-loss record to begin the year.

The 28-year-old American was made to do it the hard way against Dodin on Wednesday, dropping the first set in a tie-break.

Stephens improved on her return in the second set, winning 73 per cent of points off Dodin's second serve before running away with the match in the last.

"It's been a rough one for me lately, so I'm really pleased to get through that, fight my way through it and make it happen somehow," Stephens said post-match.

FORMER MAJOR WINNER GONE

Two-time grand slam winner Kuznetsova was the major first-round casualty, going down 2-6 6-2 6-1 to France's Alize Cornet.

Kuznetsova, who is now ranked 35th in the world, bows out with Cornet to face ninth seed Petra Kvitova.

Collins got past France's Kristina Mladenovic 6-3 6-3 with the 40th-ranked American setting up a second-round clash with 32nd seed Veronika Kudermetova.

Wang, ranked 38th in the world, also progressed despite dropping a set in a 6-1 3-6 6-3 win over Spanish qualifier Aliona Bolsova.

SECOND-ROUND MATCH-UPS

The round of 64 will commence on Thursday, with third seed Halep to face Garcia who got past another Romanian, Mihaela Buzarnescu 6-1 6-2.

Top seed Barty will be in action against Slovakia's Kristina Kucova, while fourth seed Sofia Kenin will take on former top-10 player Andrea Petkovic.

Second seed Osaka has an assignment against 77th-ranked Australian Ajla Tomljanovic, while 14th seed Victoria Azarenka is already into the third round with opponent Laura Siegemund withdrawing after her win on Tuesday.

Serena Williams showed there would be no letting up in her relentless pursuit of tennis history as she hit the practice courts with one of the biggest names on the men's tour.

A semi-final defeat to Naomi Osaka at the Australian Open was the latest blow for Williams in her attempt to match Margaret Court's record of 24 grand slam titles.

Stuck on 23 since winning at Melbourne Park in 2017, Williams has gone repeatedly close in the subsequent years without getting her hands on a major trophy.

She took to the courts with Bulgarian ace Grigor Dimitrov, a beaten quarter-finalist in Australia and former world number three, as part of her continuing bid to keep improving and stay focused on those title goals.

Dimitrov could not resist boasting about the prowess of the player he was hitting with, posting a video of their session and writing on Instagram: "My practice partner is better than yours."

He added a goat emoji, signalling his belief that Williams is the greatest of all time.

Williams gestured a fond goodbye to the Australian Open crowds after her loss to Osaka, and became tearful in an after-match news conference when asked if it was a final farewell.

"I don't know. If I ever say farewell, I wouldn't tell anyone," said the 39-year-old.

Her next appearance on tour is expected to be at the Miami Open, starting on March 23, a tournament which has confirmed Williams, Osaka, Bianca Andreescu and Simona Halep among its field.

There was a little sibling envy from Venus Williams on Sunday when she questioned where Serena and Dimitrov were rallying.

"Omg are you guys hitting now? Where is my invite??" Venus wrote.

The next grand slam on the calendar is the French Open, beginning on May 23, while Serena may see Wimbledon, beginning on June 28, as providing her best chance of another slam.

She has won seven times at the All England Club, two behind the record held by Martina Navratilova.