Osaka holdspublished at 20:20 British Summer Time
Osaka 6-3 3-2 Gauff*
Gauff takes the first point off Osaka's serve for the first time in the match but the Japan player wins the next four points to take another hold.
No sign of a dip from her yet.

Naomi Osaka in superb form to beat third seed Coco Gauff 6-3 6-2 and reach first Grand Slam quarter-final since 2021
Wimbledon champion Iga Swiatek beats 13th seed Ekaterina Alexandrova 6-3 6-1 on Louis Armstrong Stadium
Felix Auger-Aliassime beats Andrey Rublev 7-5 6-3 6-4 to reach last eight
Alex de Minaur beats qualifier Leandro Riedi 6-3 6-2 6-1 to book quarter-final tie with Auger-Aliassime
Defending men's champion Jannik Sinner plays Alexander Bublik in night session
Sean Kearns, Jess Anderson, Alex Brotherton, Sophie Brown and Henry Cowling
Osaka 6-3 3-2 Gauff*
Gauff takes the first point off Osaka's serve for the first time in the match but the Japan player wins the next four points to take another hold.
No sign of a dip from her yet.
Munar 3-6 Musetti
Easy as you like from Lorenzo Musetti.
The Italian takes the first set, breaking his Spanish opponent twice along the way.
Jaume Munar's body language was worrying towards the latter part of that set, and he was hunched over at the baseline by the time Musetti had taken his seat after winning the first set.
Annabel Croft
Former British number one on BBC Radio 5 Sports Extra and BBC Sounds
It feels like a long way back for Coco Gauff.
Even though it's tight in this second set, it feels like a lot will have to change in her confidence to turn this around.
*Osaka 6-3 2-2 Gauff
Another straightforward hold for Gauff on the board and we remain on serve in set two.
Plenty of encouragement from her coaching box as she aims to make a dent in the Osaka serve.
Annabel Croft
Former British number one on BBC Radio 5 Sports Extra and BBC Sounds
Much more positive game that for Coco Gauff, to lay down the psychological markers to Naomi Osaka that she's here fighting and that she's going to try to seek solutions to her game.
Osaka 6-3 2-1 Gauff*
Bit of a statement game that from Osaka.
Gauff might be growing into this but Osaka sends a message with a brutal hold to love.
Jonathan Jurejko
BBC Sport senior tennis reporter at Flushing Meadows
This feels to me like the best level Naomi Osaka has produced since she returned to tour.
Certainly, if she sees this encouraging start through, it will be the former world number one's best win by ranking in SIX years.
A more measured approach to her baseline game is reaping rewards.
Osaka has drawn mistakes from the clearly-uncertain Gauff, whose forehand breaking down in the rallies has been the telling factor so far.
Annabel Croft
Former British number one on BBC Radio 5 Sports Extra and BBC Sounds
I think Coco Gauff is someone who absorbs the disappointment of the crowd.
When she feels like she's letting them down, it gets on top of her.
She's somebody that takes it to heart when she's not playing well.
*Osaka 6-3 1-1 Gauff
Osaka tries to whip her forehand down the line but can't keep it inside the lines. That's just one of a couple of misses from the two-time champion and Gauff regroups to get herself on the board in set two.
Munar 2-3 Musetti*
On Louis Armstrong Stadium, another men's fourth-round match is under way.
Lorenzo Musetti, the 10th seed, has settled the quicker - as you'd suspect.
Jaume Munar gets the hold to 30 and boy did the Spaniard need that to get to 3-2 behind.
It's been a tough start for the world number 44, who finds himself a break down in this first set.
Osaka 6-3 1-0 Gauff*
Gauff got herself back into the game there but it wasn't quite enough and Osaka takes the hold.
She looks really frustrated.
Annabel Croft
Former British number one on BBC Radio 5 Sports Extra and BBC Sounds
I've never seen Coco Gauff do that, it looks like she may have cracked the racquet on the floor.
She may have to change that racquet because she gave it an almighty smack.
If she could have steam coming out of ears, she would - that's where she's at right now.
She's fuming.
*Osaka 6-3 0-0 Gauff
Eek. Gauff thrashes her racquet into the Arthur Ashe court after another error.
This could very well slip away if the American isn't careful but she regains her composure to take a couple of points.
*Osaka 6-3 0-0 Gauff
Contrasting attitudes here on each side of the court.
While Gauff cuts a frustrated figure, waving her racquet around in exasperation as she misses the forehand, Osaka is bouncing up and down on the baseline and often has a smile on her face.
Annabel Croft
Former British number one on BBC Radio 5 Sports Extra and BBC Sounds
Coco Gauff's return-of-serve problem has got to change, because she's going to have no chance if she can't get the ball back into play.
They're not even overly stressing serves from Naomi Osaka - the ones Gauff is missing aren't balls that are forcing misses.
She's got time with them, she's just not trusting herself.
Osaka 6-3 Gauff
A brilliant set of tennis from Naomi Osaka and she takes the opening set with ease.
Osaka has looked seriously back to her best in this tournament so far.
Gauff will have to come from behind if she is to reach the quarter-finals.
Jonathan Jurejko
BBC Sport senior tennis reporter at Flushing Meadows
Having said that about the divided support, it is Gauff who hears an encouraging ovation as she step onto the baseline to serve to stay in the set.
More vocal support comes after a pesky double fault...
Osaka 5-3 Gauff*
Gauff hits an ace but then a double fault and that hands Osaka a 15-30 lead.
A loose forehand later and Osaka has two set points.
Osaka 5-3 Gauff*
Osaka rattles off another no-nonsense hold to 15 and she looks pretty unshakeable at the moment.
Gauff will serve to stay in the set.
Jonathan Jurejko
BBC Sport senior tennis reporter at Flushing Meadows
A tap of the strings from Osaka tells you how good a forehand winner from Gauff is in the seventh game.
Gauff is certainly starting to warm to the task after losing serve early doors.
A packed crowd on Arthur Ashe Stadium is engrossed - but feels like the fans are slightly conflicted in their support.
Osaka plays under the Japanese flag, of course, but is a popular figure in New York City having grown up here in Queens.