A "battle-tested" Coco Gauff showed grit to keep her bid for a second US Open title alive with victory over Paula Badosa in the second round.

Fourth seed Gauff had lost her past two matches against Spanish former world number two Badosa, but showed impressive composure in a tough encounter at Flushing Meadows in New York.

American Gauff was twice a break up in the second set and served for the match at 6-5, only to put a volley into the net to send it to a tie-break.

After a quick yell of "why?" towards her team, Gauff reset and was solid to close out victory on a second match point.

Gauff's improved second serve was on show throughout - she won 57% of points behind it and committed only five double faults.

"I saw the draw - it is definitely not someone you want to play in the second round," Gauff, 22, said.

"But I need matches like this to build my confidence and I'm happy with how I managed today.

"Getting through in straight sets too makes a big difference. Yes, I was battle-tested, but I think it was a good battle where I wasn't out on the court for three hours."

Gauff would need to win the title and hope Elena Rybakina does not reach the semi-finals if she is to become world number one.

Kazakhstani second seed Rybakina claimed a 6-2 6-4 victory over Spain's Jessica Bouzas Maneiro, meaning the women's top 10 in the WTA rankings have reached the third round of a Grand Slam for the first time since Wimbledon in 2009.

Earlier on Thursday, Naomi Osaka recovered from a second-set blip to overcome Czech Katerina Siniakova 6-2 5-7 6-1.

Two-time winner Osaka served for a place in the third round during the second set but lost four straight games as she squandered a 5-3 lead.

However, after leaving the court to reset, the Japanese 28-year-old overpowered top-ranked doubles player Siniakova in the decider.

After Osaka walked out for her first-round match in an outfit inspired by NBA legend Allen Iverson, she returned to the court on Thursday wearing a white dress embroidered with tennis racquets.

The 2018 and 2020 US Open winner took a commanding first set in half an hour, and looked on course for a straightforward victory after breaking serve for a 4-2 lead in the second.

That marked the start of four successive breaks of serve - including Osaka failing to close out the match - and Siniakova took full advantage as the 13th seed's consistency dipped.

But Osaka, who made 20 of her 29 unforced errors in the second set, returned to her former levels and won six of the final seven games to complete victory in two hours two minutes.

"The match was definitely really tough. I was a little bit too hard on myself after opportunities in the second set," Osaka told the crowd inside Arthur Ashe Stadium.

"I took the bathroom break, regrouped a little, came back and just tried to have no regrets."

Poland's Iga Swiatek, a six-time major winner and former world number one whose sole US Open triumph arrived in 2022, beat Argentina's Nadia Podoroska 6-3 6-2 to set up a meeting with Czech Marie Bouzkova.

American former runner-up Madison Keys saved five match points to triumph 5-7 6-4 7-6 (10-5) in a thrilling match with Hungary's Anna Bondar.(BBC)