Gary Rose, Michael Beardmore, Josef Rindl and Adam Chowdhury
All times stated are UK
Coming up later and tomorrow
Right, that's the end of our live text coverage for the day but there are still some big names to come at Flushing Meadows tonight.
Former world number one Caroline Wozniacki continues her comeback as she meets 11th seed Petra Kvitova in a mouth-watering match on Arthur Ashe Stadium.
On Louis Armstrong Stadium, there's fourth seed Elena Rybakina against Ajla Tomljanovic and then in the men's draw Taylor Fritz takes on Juan Pablo Varillas of Peru.
You can follow the scores in those matches here.
And please join us again right here on Thursday when we'll have six Britons - including Andy Murray, Cameron Norrie and Katie Boulter - among those in second-round singles action.
Tsitsipas out, Djokovic through
The biggest shock of day three was seventh seed Stefanos Tsitsipas being beaten by qualifier Dominic Stricker in the second round of the US Open.
World number 128 Stricker (pictured) came out on top of a four-hour epic 7-5 6-7(2-7) 6-7(5-7) 7-6 (8-6) 6-3.
Tsitsipas of Greece was serving for the match in the fourth set but his Swiss opponent fought back to force a third tie-break. Stricker then won the deciding set to progress to round three.
No such problems for world number one Novak Djokovic, who cruised through 6-4 6-1 6-1 against Spain's Bernabe Zapata Miralles.
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GB's Miyazaki bows out to Bencic
British qualifier Lily Miyazaki saw her memorable US Open run come to an end with a second-round exit against Olympic champion Belinda Bencic.
Miyazaki, 27, had never qualified for a Grand Slam main draw until she won three matches to reach the first round.
The British number seven backed that up with a straight-set victory over Russia's Margarita Betova.
But Bencic was a different proposition and Miyazaki, despite frustrating the Swiss 15th seed, was beaten 6-3 6-3.
"It was a tough match, but I'm still super proud of these couple of weeks," Miyazaki said.
Read Jonathan Jurejko's full report here.
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Gauff wins teen tussle with Andreeva
American sixth seed Coco Gauff progressed to the third round of the US Open after beating fellow teenager Mirra Andreeva in straight sets.
Gauff, 19, beat her Russian opponent 6-3 6-2 in New York to keep alive her hopes of a first major singles title.
World number one and defending champion Iga Swiatek was made to work hard for a 6-3 6-4 victory by Australia's Daria Saville.
And Belgium's Elise Mertens came from a set down to win a thriller against American Danielle Collins 3-6 7-6 (9-7) 6-1.
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- See AlsoUS Open: Inspired Gauff beats Wozniacki to reach quarter-finalsZverev erreicht das Viertelfinale der US Open - nun gegen Taylor FritzUS Open LIVE: Alexander Zverev vs Taylor Fritz - quarter-final live text & radio commentaryEmma Navarro reaches her first Grand Slam at the U.S. Open with win over Paula Badosa - TPR: The Public's Radio
Doubles delight for Brits
Tuesday was a brilliant day in the singles for British tennis with six wins from six - and Wednesday has been a cracking day in the doubles.
Joe Salisbury and American partner Rajeev Ram - the defending and two-time US Open champions - beat Italians Simone Bolelli and Andrea Vavassori 6-3 7-6 (7-2).
Briton Jamie Murray and his New Zealand partner Michael Venus, the 12th seeds, won 7-6 (7-3) 7-6 (7-3) against Ecuadorian Gonzalo Escobar and Kazakh Aleksandr Nedovyesov to advance.
British duo Julian Cash and Henry Patten also made it into round two, beating Americans William Blumberg and Steve Johnson 7-5 6-1.
There was also victory for Lloyd Glasspool as he and Finnish partner Harri Heliovaara - the 13th seeds - beat Brazilian Marcelo Melo and Australian John Peers 6-4 7-6 (7-4).
Read the full story here.
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'I still have the hunger and desire' - Djokovic
Djokovic 6-4 6-1 6-1 Zapata Miralles
Novak Djokovic speaking after his second-round win against Bernabe Zapata Miralles:
"It has been a tough match, especially in the first set with the conditions. When we had the entire court in the shadow it was a bit easier but still a lot of humidity. It's the same for both players so you have to embrace it and accept it. I'm very pleased with the way I ended the match."
"You can't always play in the ideal conditions. Once you're in the tournament, you need to be ready, even if you think you're not."
"I still feel like I can play better but I'm happy to be back playing in New York. That's what gives me strength at 36 years of age. I still have the hunger and the desire to play my best tennis on this court."
"Every single match I play myself the most, in my mind. If I win this battle, then I win the battle outside against the opponent."
Post update
Djokovic tells Arthur Ashe "after 20 years I still have the hunger and desire to keep coming to New York".
Full quotes from him to come.
'Djokovic sprinted away'
Djokovic 6-4 6-1 6-1 Zapata Miralles
Mark Woodforde
17-time Grand Slam doubles champion on BBC Radio 5 Sports Extra
The battle was there in the first set. Bernabe Zapata Miralles was trying to do his best and stay with Novak Djokovic in the first set but once that break of serve was conjured by Djokovic, he sprinted away.
Game, set and match Djokovic
Zapata Miralles 4-6 1-6 1-6 Djokovic
Novak Djokovic touches the court and then salutes to the crowd after he wins his 72nd match on Arthur Ashe Stadium.
The Serb gets over the line with yet another forehand winner. He was tested today by Spaniard Bernabe Zapata Miralles who made a great account of himself.
But Djokovic was another level.
Triple match point Djokovic
Zapata Miralles 4-6 1-6 1-5 Djokovic*
Djokovic flicks another forehand winner to go up 40-0. Three match points.
Djokovic breaks and will serve for match
Zapata Miralles 4-6 1-6 1-5 Djokovic*
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Another smashing winner from Novak Djokovic who has now won five five of Bernabe Zapata Miralles' last six service games.
The three-time champion will serve for the match.
Break point Djokovic
*Zapata Miralles 4-6 1-6 1-4 Djokovic
Boom! A fabulous Novak Djokovic return takes us to 30-40 and the Serb is on the brink of the third round.
'I think Andy will forgive me!'
Swiatek 6-3 6-4 Saville
World number one Iga Swiatek, speaking in her on-court interview about victory over Daria Saville:
"It wasn't easy but I'm happy I tried to play my game and play aggressively with a lot of intensity and I'm just happy to be in the third round."
On Andy Murray saying he would love to be her mixed doubles partner:
"I love that he said that, it was a dream come true because I watched Andy when he was younger and he always had such a good game and is a really cool person as well, so humble and down to earth.
"I wish I could play mixed doubles but for me singles is enough especially with such an intense and long season so I will just focus on singles and I think Andy will forgive me! I'll talk to him!"
Sounds like a caring 'let's just be friends' letdown, Andy, sorry...
Post update
Jonathan Jurejko
BBC Sport at Flushing Meadows
BBC SportCopyright: BBC Sport
The man of the moment!!
Swiss qualifier Dominic Stricker looks pleasantly bewildered as he heads back to the locker room.
The 21-year-old smiles broadly as he is ushered through the fans, all desperate to get a selfie with him, by a gang of burly security guards.
Once back into an accredited area, he receives more congratulations and dissects his performance with his team.
A day he will never forget.
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CannyJimKenny: Yet another humiliation for Tsitsipas. The years are slipping away now.
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Djokovic holds
*Zapata Miralles 4-6 1-6 1-4 Djokovic
Even Bernabe Zapata Miralles is applauding Novak Djokovic now as the three-time champion holds to 15 with a pinpoint backhand volley, stretching to his left.
Djokovic breaks
Zapata Miralles 4-6 1-6 1-3 Djokovic*
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Novak Djokovic can see the finish line now as Bernabe Zapata Miralles slices a backhand wide.
The Spaniard has called most of the shots in this set, but finds himself behind thanks to Novak's pure efficiency.
Break point Djokovic
*Zapata Miralles 4-6 1-6 1-2 Djokovic
Back to Arthur Ashe and a long forehand from Zapata Miralles gives Djokovic break point.
Game, set and match - Swiatek
Swiatek 6-3 6-4 Saville
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A big serve down the middle is unreturnable and the world number one and defending champion marches on.
But while Iga Swiatek will take the plaudits, we have to praise Daria Saville too - the Aussie really made her illustrious opponent work so hard for that win.
Match point Swiatek
*Swiatek 6-3 5-4 Saville
The world number one does what world number ones often do from 0-30 down.
Thrive. Two big-hitting points get her back level in the game and, after Saville somehow retrieves a bunch of blistering shots, Swiatek puts away a big backhand to bring up match point...
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