The 23-time Grand Slam champion reached the third round of the joint Association of Tennis Professionals (ATP) and Women's Tennis Association (WTA) tournament - moved from Cincinnati to New York due to the coronavirus pandemic - with a battling 7-6, 3-6, 7-6 victory.

Rus served for the match at 6-5 in the fifth before the 38-year-old American rallied to close out a nervy win at the Billie Jean King National Tennis Centre.

Williams - twice a winner of the event, also called the Western and Southern Open - will face Greece's 13th seed Maria Sakkari in the third round.

World number 10 Naomi Osaka of Japan fought back to overcome Karolína Muchová of the Czech Republic 6-7, 6-4, 6-2 in her first match since the resumption of the WTA Tour following an enforced break caused by the COVID-19 crisis.

In the men's draw, world number one Novak Djokovic defeated Ricardas Berankis of Lithuania 7-6, 6-4.

It was far from straightforward for the Serbian, however, as he struggled with neck pain during the second-round match.

Djokovic, a 17-time Grand Slam champion, will take on Tennys Sandgren of the United States in round three.

Austrian Dominic Thiem suffered a shock exit as he was beaten 6-2, 6-1 by Djokovic's compatriot Filip Krajinović.

Former world number one and three-time Grand Slam winner Andy Murray recorded his first victory over a top-10 player since 2017 as he ousted Alexander Zverev.

Murray, the current world number 129, won 6-3, 3-6, 7-5 to set up a meeting with Canada's Milos Raonic.

The Western and Southern Open is usually held in Cincinnati but was moved to Flushing Meadows to create a two-tournament safety bubble, which also includes the US Open, due to begin at the same venue next Monday (August 31).

The competition is an ATP Masters 1000 event and WTA Premier 5 tournament.