Williams, 43, fought back from a double breakdown in each set to win 6-4 7-5 against 16th-ranked Kudermetova.

The seven-time major singles champion smiled broadly as she celebrated winning at a US tournament for the first time in more than three years.

“I love this game, it’s what I do,” said Williams, who is ranked 533rd.

“The last few years have been difficult in terms of injuries but I love to be out here, be strong and be myself. I’m getting there.”

Williams will play China’s Qinwen Zheng or Belarus’ Aliaksandra Sasnovich in the second round.

The former world number one will look to win back-to-back matches on the WTA Tour for the first time since the 2019 event in Cincinnati.

That was also the tournament when she last won against a top-20 opponent, beating then world number five Kiki Bertens on her way to the quarter-finals.

Later on Monday, Wimbledon champion Marketa Vondrousova plays fellow Czech Katerina Siniakova, while Danish former number one Caroline Wozniacki continues her comeback after retirement against France’s Varvara Gracheva.

Wozniacki was supposed to face Ukraine’s Elina Svitolina, but the Wimbledon semi-finalist – who has also recently returned to the tour after having a baby – pulled out with a foot injury.

In the men’s draw, British number two Dan Evans plays Italy’s Lorenzo Musetti in his opening match.

The Western and Southern Open in Cincinnati is one of the key tournaments on the American hard-court swing which culminates at the US Open.

The final Grand Slam event of the season starts in New York on 28 August.

British women’s number two Jodie Burrage, who has direct entry for the main draw at Flushing Meadows, continued her preparations with a 6-4 6-2 win over Russian fifth seed Diana Shnaider at the Golden Gate Open.

But Heather Watson lost 6-2 6-4 to Belarusian Iryna Shymanovich at the Californian event.

Williams, 43, slipped early in the first-round match against Ukraine’s Elina Svitolina, leading to fears she might have to retire injured.

The five-time champion did continue and pushed Svitolina before losing 6-4 6-3.

“It was bad luck for me,” Williams said. “I can’t believe it happened. I’m still trying to process it.”

Williams, who started the match with heavy strapping on her right knee, showed undiminishing determination and courage to fight through her fitness problems before succumbing to 2019 semi-finalist Svitolina.

After a record 24th Open era appearance in the Wimbledon singles ended, Williams received a standing ovation by a crowd unsure how long she has left at the top level.

The fact she was able to finish the match, despite limping heavily around the court, felt remarkable.

Williams’ defiance not to quit was warmly appreciated by the Wimbledon crowd, who willed her on throughout an entertaining contest.

The former world number one first played at the All England Club in 1997 and, as she remains coy about her retirement plans, it remains to be seen how many more times she will return to the scene of some of her greatest triumphs.

“What makes this one hard to process is I’ve had so many injuries. I’ve been missing from tour for quite a while. This is not what I want for myself,” said Williams, who was playing in only her sixth match this year after being given a wildcard.

“This kind of fall, I didn’t do anything wrong. I just went for the ball. There’s nothing I can really do about it. Those kinds of things are hard to process emotionally, mentally and physically on the court.”

Down but not out – Williams shows her mettle

Williams walked gingerly when she came out on to court, having struggled with the knee injury earlier in the British grass-court season at Birmingham.

The veteran showed she had lost none of her shot-making ability, using her colossal serve and forehand to good effect as she broke for a 2-0 lead.

“I was literally killing it, then I got killed by the grass. I felt like I was in great form and in great form in the match,” Williams said.

The complexion of the match altered in a moment, leaving those watching on Centre Court fearing the worst.

In the third game, Williams slipped on the grass as she approached the net, letting out a sharp scream which silenced the stadium.

Umpire Marija Cicak raced down to the court to check on her condition, with a concerned Svitolina coming around the net.

There was an anxious atmosphere as fans feared the worst, many who will have remembered her younger sister Serena slipping on the lush Centre Court grass in 2021 and having to retire injured.

“I’m not sure what I’ve done. I’ll have to investigate it. It was quite painful,” Williams said.

“Afterwards it was very hard to focus on what I was doing.”

In what seemed remarkable given the gravity of her reaction, and the increasingly-restricted movement, Williams not only carried on but continued to keep in touch with 28-year-old Svitolina.

Heavy shots reminiscent of her peak flashed past the Ukrainian, who had to fend off two break-back points before sealing the first set at the second opportunity.

Even when Svitolina, who is still continuing her comeback after giving birth last October, threatened to run away with the second set, Williams would not roll over.

Trailing 5-1 and with the crowd willing her on, she dug in again to hold serve and then broke for 5-3.

But Svitolina, who did well to maintain her focus in the difficult circumstances, took her opponent’s serve again for the match after winning a line-call challenge that left Williams smiling ruefully.

“It is always very tough to play against Venus, it was a really special moment to play here today on a special court and a big legend,” said Svitolina, who is ranked 76th in the world.

“It was an unbelievable feeling.”

Teaming up for the first time since 2018, and probably the last time, they lost 7-6 (7-5) 6-4 to Czechs Lucie Hradecka and Linda Noskova.

Together, the American greats have won 14 Grand Slam doubles titles.

Serena Williams, 40, is due to retire after the tournament, while the future plans of elder sister Venus, at 42, remain unknown.

Serena plays Australia’s Ajla Tomljanovic in the third round of the women’s singles on Friday, but Venus was knocked out in the first round.

Opening the night session on Arthur Ashe Stadium on Thursday, the sisters failed to convert two set points on their opponents’ serve at 5-4, with break points having earlier gone begging for both pairs.

Hradecka and Noskova edged the ensuing tie-break on their first set point, with 37-year-old Hradecka wrapping up proceedings with a powerful backhand down the line.

She and Noskova, 20 years her junior, went on to dominate the second set, sealing an early break. They soon held double break point for 4-0 but Noskova couldn’t convert from close to the net in a slice of luck for the Williams sisters, who went on to hold and end a five-game losing streak.

They went on to break back but it proved in vain as Hradecka and Noskova broke their serve again on their second match point.

The Williams sisters remain the most recent women’s doubles team to hold all four major doubles titles at once with wins at Wimbledon and the US Open in 2009, followed by triumphs at the Australian Open and French Open in 2010.

The last of their Grand Slam doubles titles together came at Wimbledon in 2016, more than 17 years after their first at Roland Garros in 1999, while they also have three Olympic doubles golds.

Venus Williams returned to action for the hard-court swing, appearing in Cincinnati, Toronto and Washington, after nearly a year off following a leg injury, and was awarded a wildcard for the US Open. She is currently ranked 1,504th in the world in the singles, while Serena is 605th.

They have a combined 30 Grand Slam singles titles, 23 of which belong to Serena.