US Open day seven - listen to BBC Radio 5 Sports Extra commentary (UK only)
LIVE: Defending champion Carlos Alcaraz 6-4 American Tommy Paul
Second seed Alcaraz bidding for third New York title and eighth major overall
Wimbledon champion Linda Noskova wins 7-5 5-7 6-4 against Marta Kostyuk to set up quarter-final with world number one Aryna Sabalenka
Sabalenka beat home hope Taylor Townsend 6-4 6-3 to continue quest for third straight title
She must win title - and hope Elena Rybakina loses before semi-finals - to keep world number one ranking
GB's Harry Patten into third round of doubles alongside Finland's Harri Heliovaara
Paul 4-6 1-4 Alcaraz*
Tommy Paul is clinging on for dear life now.
He reaches Carlos Alcaraz's drop shot but the Spaniard then reads the passing shot and produces a stunning reaction volley and brings up three break points.
Paul digs deep to save all three, only for Alcaraz to bring up another with a magnificent backhand down the line on the move for a winner.
The American saves that with a massive 138mph serve but on we go...
Kostyuk 5-7 7-5 4-6 Noskova
Jeff Tarango
Former American tennis player on BBC Radio 5 Live
Now Kostyuk looks tired. It's almost like the relief of it, she can show she's tired. This crowd really favouring Kostyuk but the Wimbledon champ shows by just pure greediness that she was going to win the match.
She didn't have a doubt whether she was going to win or lose, it was just how long was it going to take.
*Paul 4-6 1-4 Alcaraz
Break consolidated this time.
Carlos Alcaraz is feeling it now. He throws in a serve and volley to give Tommy Paul something else to think about, moving up 40-15.
The Spaniard then drills a forehand down the line before moving in and creating a brilliant angle to go cross-court.
Paul can barely reach it and he can feel the second set slipping away from him.
Kostyuk 5-7 7-5 4-6 Noskova
Image source, ReutersLinda Noskova drops to the floor.
On a sixth match point, about an hour after her first, the Wimbledon champion has done it!
A first US Open quarter-final is hers after surviving an emotional rollercoaster against Marta Kostyuk, who certainly played her part in a thrilling match.
Paul 4-6 1-3 Alcaraz*
Carlos Alcaraz wastes no time in regaining the break advantage in the second set!
With Tommy Paul's serve faltering, Alcaraz brings up two more break points with a gorgeous lob.
He then finds the line with a stinging forehand - the crowd can't believe it's in and Paul does well to get it back over the net... but it drops wide and the defending champion reasserts his control.
Kostyuk 5-7 7-5 4-5 Noskova*
Marta Kostyuk is hanging in here... again! Linda Noskova covers her face with her hand after missing two more match points - her third and fourth overall after she failed to seal victory in the second set.
This is agony for the sixth seed, but it gets worse as Kostyuk reaches break point.
Noskova holds her nerve to save that, and earn a fifth match point.
Kostyuk says no again! It's hands-on-face time again for Noskova. Surely this can't slip away again?!
*Paul 4-6 1-2 Alcaraz
Image source, Getty ImagesTommy Paul needed that!
He gets the break back immediately, just at the moment it seemed the match was getting away from him.
Carlos Alcaraz saves the first break point but is wide with a forehand on the second. Back on serve in the second set.
*Paul 4-6 0-2 Alcaraz
Now then...
Carlos Alcaraz finds the net with a backhand and Tommy Paul has two break points.
Big moment in this match, especially for the American, you feel.
Paul 4-6 0-2 Alcaraz*
David Law
Commentator on BBC Radio 5 Sports Extra
Alcaraz is turning it on here, it's quite something to behold.
Tommy Paul just smashed down a 136mph serve, Alcaraz got it back, another from Paul and a forehand that was probably about 136mph from Alcaraz.
He's broken for two love, he's roaring away from Paul now.
Kostyuk 5-7 7-5 4-5 Noskova*
Once again, Linda Noskova is one game away from a place in the US Open quarter-finals.
Can she get over the line this time?
Marta Kostyuk will not go quietly. Just as she did late in the second set, the 11th seed holds serve to give herself the chance to test Noskova's nerves.
Paul 4-6 0-2 Alcaraz*
Image source, Getty ImagesThat's extraordinary from Carlos Alcaraz!
Somehow he gets a 136mph serve back and then follows it up with a rocket cross-court forehand.
It just finds the line with Tommy Paul helpless and that brings up three break points.
He needs just one, coming in to slap a forehand winner. Worrying moments for Paul.
*Paul 4-6 0-1 Alcaraz
The chance was there for Tommy Paul, just briefly.
Up 15-30, the American 20th seed gets a look at a second serve but the return lets him down.
Carlos Alcaraz comes through to hold and keep the momentum.
Kostyuk 5-7 7-5 3-4 Noskova*
Jeff Tarango
Former American tennis player on BBC Radio 5 Live
When Kostyuk won that second set she was all smiles, giggles and laughing and her smile has really gone away.
Kostyuk 5-7 7-5 3-4 Noskova*
Image source, Getty ImagesWow, this is tense!
Marta Kostyuk offers an immediate response to falling behind in the third set - although she is certainly helped by a couple of big misses from Linda Noskova.
But Kostyuk can't build on that and is soon facing more break points. The Ukrainian saves the first two, but a big forehand from Noskova puts the sixth seed back in charge.
Paul 4-6 0-0 Alcaraz*
Image source, Getty ImagesCarlos Alcaraz turns it on when it really matters at the end of the set.
He ramped up the pressure on Tommy Paul and the American just couldn't cope on this occasion.
He saves the first set point with a huge 136mph ace out wide and is aggressive on the next point, too, as he knows he needs to be.
But his blistering forehand is just wide and the defending champion is a set to the good.
Paul 4-5 Alcaraz*
Jeff Tarango
Former American tennis player on BBC Radio 5 Live
Paul has just been shaken a little bit by what Alcaraz has just done. Paul's done nothing wrong, he just can't live with this level from Alcaraz.
Paul 4-5 Alcaraz*
"Vamos!" cries Carlos Alcaraz.
He's on the attack against the Tommy Paul serve and moves up 0-30 again.
Paul finds the net again and Alcaraz has three break - and set - points.
*Paul 4-5 Alcaraz
Pressure on after losing the first point on serve at a crucial stage in the set?
Not if you're Carlos Alcaraz. He comes in behind a big serve out wide and powers a drive volley down the line for a winner.
He goes on to hold to 15 and Tommy Paul will serve to extend the first set.
Kostyuk 5-7 7-5 2-3 Noskova*
Who will deliver the next twist in this engrossing fourth-round contest?
Marta Kostyuk has already escaped two match points to recover from 5-4 down in the second set and take her match against Wimbledon champion Linda Noskova to a decider.
Noskova, desperately needing to quickly move on from that disappointment, is the first to come under pressure in the third set but holds from deuce.
The sixth seed closes here eyes and breathes a sigh of relief.
Then, it's Kostyuk's turn, as a 40-15 lead evaporates.
A wide forehand gives Noskova the first opportunity of this set... and concedes with another miss!
Kostyuk can't believe it. She's going to have to come from behind again.
Image source, Getty ImagesPaul 4-4 Alcaraz*
Tommy Paul gets himself out of trouble.
He wins the next four points and still we haven't seen so much as a single break point.
Carlos Alcaraz will be disappointed because he had a couple of looks at the second serve but couldn't capitalise.
