Barty defeated Russia’s Vera Zvonareva in straight sets but was forced to dig deep in the second set, with the top seed broken while serving for the match and being forced into a tiebreak, which she won to seal a 6-1, 7-6 victory at Flushing Meadows.

Fourth seed Karolína Plíšková of the Czech Republic was also a straight sets winner, beating home player Catherine McNally 6-3, 6-4.

Canadian Bianca Andreescu, seeded sixth and who won the US Open in 2019 in her only previous appearance in the tournament, becoming the only player to win the Grand Slam on her main draw debut.

The 21-year-old faced a tough test against Switzerland’s Viktorija Golubic, but triumphed 7-5, 4-6, 7-5 to reach the second round.

World number eight Iga Świątek of Poland triumphed over American qualifier Jamie Loeb 6-3, 6-4 to ensure safe passage, while the 10th seed Petra Kvitová of Czech Republic started with a win over Slovenia’s Polona Hercog.

Belinda Bencic, the 11th seed from Switzerland, and recent women's Olympic singles champion at Tokyo 2020, also triumphed, beating Arantxa Rus of The Netherlands 6-4, 6-4.

Russia’s Anastasia Pavlyuchenkova overcame American Alison Riske in what was a fruitful day for the seeded players.

The 17th seed Maria Sakkari of Greece defeated Marta Kostyuk of Ukraine 6-4, 6-3, while 24th seed Paula Badosa of Spain beat Belgium’s Alison Van Uytvanck by the same scoreline.

Karolína Muchová of Czech Republic, seeded 22nd, was perhaps the biggest casualty of the day and the first round, losing in straight sets to Spain’s Sara Sorribes Tormo 2-6, 6-7.

Qualifier Emma Raducanu of Britain marked her first appearance in the US Open main draw with a straight sets victory over Swiss lucky loser Stefanie Vögele 6-2, 6-3.

The second round is due to get underway tomorrow, with defending champion Naomi Osaka of Japan in action against Serbia’s Olga Danilović, and second seed Aryna Sabalenka of Belarus facing Slovenia’s Tamara Zidanšek in the bottom half of the draw.