World number one Ashleigh Barty recovered from a second-set stutter to beat Russian Vera Zvonareva for a place in the US Open second round.

Zvonareva - a 2010 US Open finalist - claimed a late break and forced a second-set tie-break but was ultimately outclassed by the Australian.

Earlier on Tuesday, Czech fourth seed Karolina Pliskova also advanced.

Olympic champion Belinda Bencic made it to the second round too as the Swiss 11th seed saw off Dutch opponent Arantxa Rus 6-4 6-4.

Pliskova powered past American Caty McNally 6-3 6-4 as she looks to improve on her Wimbledon final defeat by Barty with a first Grand Slam title.

Barty, 25, did not compete at last year's US Open because of concerns about travelling during the coronavirus pandemic and she said she was "exceptionally proud" of that decision.

"I was disappointed not to be able to play last year but this year with fans has made it all the better, the city is buzzing and it is nice to share this with everyone here today," she said.

"We made the right decisions for us - we trained and got ready, came into this year with the attitude it was going to be a different adventure for us, but it has been really enjoyable right from the start."

Pliskova, whose only other major final appearance came at the 2016 US Open, will face American Amanda Anisimova next, while Barty plays Denmark's Clara Tauson and Bencic is against Italy's Martina Trevisan.

On Monday, Naomi Osaka and Simona Halep were among seven women's Grand Slam champions to advance to the second round.