The British 11th seed was given one of the harder unseeded players in the draw, with world number 40 Cornet making it to a Grand Slam quarter-final for the first time in her career earlier this year at the Australian Open - another hard-court event.

Cornet celebrated her 63rd consecutive Grand Slam appearance - a new women's singles record dating back to 2007 - with a 6-3, 6-3 victory.

"This one obviously hurts a bit because it's my favourite tournament and there are a lot of emotions in the past year," said Raducanu after the match, with the teenager's year being plagued by niggling injuries.

"I'm proud for putting myself out there every match, every day, knowing I'm pushing myself to be the best I can."

Two-time US Open winner Naomi Osaka was also eliminated in her opener, having only returned to the professional circuit in San Jose at the start of August after months out with injury.

Despite a positive start, the Japanese star lost to American 19th seed Danielle Collins 7-6, 6-3.

Wimbledon champion Elena Rybakina exited in the first round too after a shock loss to qualifier Clara Burel.

The Russian-born Kazakhstani went down 6-4, 6-4 to world number 131 Burel of France.

Earlier, women's world number one Iga Świątek of Poland won in straight sets against Italy's Jasmine Paolini to set up a meeting with Sloane Stephens of the United States next.

This means she is the only Grand Slam winner from the past 12 months to remain in the women's singles tournament, as Australian Open Ash Barty has retired.

Świątek, who spoke out against the different balls provided for female players at Flushing Meadows, beat Paolini 6-3, 6-0 in little more than an hour.

Venus Williams was not able to replicate her sister Serena's performance from day one as she lost to Belgium's Alison Van Uytvanck 6-1, 7-6.

Meanwhile, Spain's ninth seed Garbiñe Muguruza secured a 6-3, 7-6 win over Clara Tauson of Denmark.

It was a happy day for Jelena Ostapenko of Latvia, who managed to defeat China's Zheng Qinwen 6-3, 3-6, 6-4 before Karolína Plíšková of the Czech Republic got the better of Pole Magda Linette 6-2, 4-6, 7-6.  

There was more joy in store for the Czech Republic as 21st seed Petra Kvitová beat Erika Andreeva 7-6, 6-0.

Andreeva, like other Russians, is permitted to play as a neutral.

Spanish teenager Carlos Alcaraz reached the second round after his opponent, Argentina's Sebastian Baez, retired.

The third seed was up 7-5, 7-5, 2-0 when Baez decided to pull out.

Fellow Spaniard Rafael Nadal dropped the first set against Australia's Rinky Hijikata, but recovered to win 4-6, 6-2, 6-3,6-3.

Neutral ninth seed Andrey Rublev survived a scare and came out on top of a thrilling five-setter against Serbian Laslo Đere.

The final score read 7-6, 6-3, 3-6, 4-6, 6-4 in the Russian's favour after three hours and 41 minutes.

The 2014 US Open champion Marin Čilić of Croatia won his battle against Germany's Maximilian Marterer 6-3, 6-2, 7-5.

Grigor Dimitrov of Bulgaria won in straight sets against American Steve Johnson.

Fellow American John Isner posted a 6-3, 6-1, 7-5 win over Argentina's Federico Delbonis while 28th seed Holger Rune of Denmark defeated 19-year-old Peter Gojowczyk of Germany 6-2, 6-4, 7-6.

Polish eighth seed Hubert Hurkacz defeated Oscar Otte of Germany 6-4, 6-2, 6-4.

Seeded Italians Jannik Sinner and Lorenzo Musetti required five sets to progress.

Eleventh seed Sinner won 5-7, 6-2, 6-1, 3-6, 6-1 against Daniel Altmaier from Germany while Musetti eliminated David Goffin of Belgium 3-6, 7-5, 6-4, 3-6, 7-6.

Finally, British seventh seed Cameron Norrie thrashed Benoit Paire 6-0, 7-6, 6-0, with the Frenchman hinting at ending the season and perhaps even his career.