World number one Ashleigh Barty staged a third-set fightback to beat Kristina Kucova at the Miami Open in her first match outside Australia for more than a year.

Barty is the defending champion having won what was then the biggest title of her career in 2019 – the tournament was not held last year – before adding a first grand slam title at the French Open.

The 24-year-old stayed at home in Australia once the coronavirus pandemic took hold and the 50-hour journey she made to Florida was her first trip away from the country since last February.

The changes to the ranking system have kept her on top despite her inactivity and Naomi Osaka winning two slam titles, but the Japanese player could reclaim the number-one spot after this tournament.

Barty struggled for form against Slovakian Kucova and trailed 5-2 in the deciding set but reeled off five games in a row to secure a 6-3 4-6 7-5 victory.

Barty said: “Just never give up. You have to be in the fight to have a chance and it’s about trying to chip away over and over. Matches like that are extremely fulfilling. Today was much more about the fight than the result but certainly happy to give myself the chance in a couple of days to go again.”

There was a much-needed win for fifth seed Elina Svitolina, who has had a difficult start to the season. The Ukrainian defeated American Shelby Rogers 3-6 7-5 6-3 to set up a third round meeting with Ekaterina Alexandrova.

Croatian Ana Konjuh, who has had a terrible time with injuries, claimed her best victory for four years by beating 18th seed Madison Keys 6-4 6-2 while seventh seed Aryna Sabalenka recovered from losing the first set to love to see off Tsvetana Pironkova 0-6 6-3 7-6 (9), saving two match points.

Simona Halep recovered from an early stumble to dispose of Caroline Garcia 3-6 6-4 6-0. She will take on Anastasija Sevastova in the third round, after the Latvian upset 31 seed Cori Gauff 1-6 6-2 6-3.

Petra Kvitova wound back the clock with a dominant 6-0 6-4 victory over Alize Cornet.

French Open champion Iga Swiatek was a 6-4 6-2 winner over Barbora Krejcikova, Angelique Kerber thumped Renata Zarazua 6-0 6-0, while there were also victories for Belinda Bencic, Johanna Konta, Jelena Ostapenko, Marketa Vondrousova and Veronika Kudermetova.