Hailey Baptiste hits a 119mph ace - the fastest of the match - but Osaka then produces a sharp return.

Baptiste commits another double fault, but Osaka spurns the chance to earn a break point by netting a simple backhand. Baptiste smashes a backhand winner and holds.

Jannik Sinner consolidates the break.

The World number one is looking extremely relaxed out there and it's a simple hold to extend his lead over the Australian.

Naomi Osaka serves up a 98mph ace, before grazing the lines with some powerful forehands.

Hailey Baptiste responds with a vicious forehand winner to take us to deuce, and then finds herself at break point as Osaka sends a backhand into the net.

Osaka produces some outrageous defensive shots - including a lob that had Baptiste scrambling - before hitting sweeping forehand winner to take the game.

*denotes next server

Russell Fuller
Tennis correspondent on BBC Radio 5 Live and BBC Sounds

Popyrin has not had an ideal start against the world number one and defending champion.

Alexei Popyrin hits in to the net to put himself under a little bit of early pressure at 30-30.

The Australian then goes long and faces the first break point of the match.

Jannik Sinner takes full advantage on the second serve and it's an early break.

Naomi Osaka begins the second set with a break.

Hailey Baptiste is really struggling to win points on her second serve - just 18% in the first set compared to 50% for Osaka.

On break point, the American double faults for the fifth time today.

Jannik Sinner gets off to the ideal start.

A simple hold of serve and the Italian is up and running.

Jannik Sinner will get us under way in this one.

* denotes next server

Naomi Osaka takes the first set as Hailey Baptiste returns long of the baseline.

The Japanese player looks strong and is making fewer unforced errors (six) compared to her opponent (11).

Image source, Getty Images

Jannik Sinner has been in magnificent form this year, having won the Australian Open and Wimbledon, either side of his three month ban from the sport.

In the other Grand Slam he lost a pulsating final against Carlos Alcaraz at the French Open, the same opponent who he had to retire against in Cincinnati and the Italian said after his first round victory that he is relieved to be back on the court.

"I'm very happy that I'm healthy again and that we did our best to be in the best possible shape here.

"Every year is different and you come here starting this tournament hopefully in the best possible way, which I have done.

"Coming back to a Grand Slam, where the emotions are still running - I'm very happy to come back here and compete against the best players in the world."

Right, next up on Arthur Ashe stadium is the small matter of Jannik Sinner.

The World number one and defending champion was not severely tested in his first-round match, needing just one hour and 38 minutes to see off Vit Kopriva and dropping only four games in the process.

Sinner retired from his Cincinnati Open final last week because of illness but showed little sign of that in a comfortable victory on Tuesday.

The Italian is likely to have a much sterner examination from Alexei Popyrin of Australia, who is ranked 36th in the world and defeated Novak Djokovic in round three of last year's US Open.

Hailey Baptiste looks to be in a spot of bother as she goes from 40-0 up to 40-30, but produces a beautifully-timed backhand drop shot to hold.

It's back-to-back points on serve from Andrey Rublev to nudge him ahead.

Tristan Boyer then looks to hold but the Russian gets a crucial mini-break.

Boyer avoids giving his opponent a look at match point but Rublev needs two holds for victory.

Naomi Osaka holds with a strong service game and is now one break away from winning the first set after 27 minutes.

Andrey Rublev starts the tie-break with a mini-break and it gives him an opportunity to kick on.

However, Tristan Boyer once again finds an instant response and Rublev then serves out the next point with Boyer following suit with a double hold to keep us on serve in the tie-break.

Break point for Naomi Osaka, and she takes it as Hailey Baptiste makes a ninth unforced error when returning Osaka's serve return.

And we are going all the way in this fourth set.

Andrey Rublev executes a simple hold and the Russian will be hoping he can put this match away in the next 10 minutes or so.

Iga Swiatek, speaking on court after beating Suzan Lamens in the second round: "I served better [in the third set] than in the previous sets. I wanted to be pretty confident with my serve and go for it. I'm happy that I closed it pretty fast, even though I lost one break.

"It wasn't an easy match and I made some mistakes. I'm happy that at the end I could be more proactive."

On the challenge of finding form again after Lamens' fightback: "I felt like it depended on me and whether I was going to make mistakes or not. Sometimes I did, I probably got a little tight in the second set and she, for sure, used the opportunity and was using her chances.

"It was not easy, but the third set is a reset. You've got to start from the beginning and I knew I could play a little more precisely, so I just tried to do that."

Hailey Baptiste has only made four first serves today, which is putting a lot of pressure on her second serve.

But she produces a timely serve to steer game four in her favour, before hitting a superb forehand winner to hold.

Her coach tells her to "keep breaking her [Osaka's] forehand down."

Osaka replies with a couple of powerful winners to hold and retake the lead.