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 former world number two Badosa, but showed impressive composure in a tough encounter.

The American 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 just 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 leave Flushing Meadows as world number one.

Second seed Rybakina continued her bid for the top ranking with a 6-2 6-4 victory over Jessica Bouzas Maneiro.

Her victory means the women's top-10 have all reached the third round of a Grand Slam for the first time since Wimbledon in 2009.

Osaka battles and Swiatek cruises

Earlier on Thursday, Naomi Osaka recovered from a second-set blip to overcome 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, the four-time major winner 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 and two minutes.

"The match was definitely really tough. I just felt like 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."

Iga Swiatek, a six-time major winner whose sole US Open triumph arrived in 2022, had no such issues.

Poland's 25-year-old former world number one defeated Argentina's Nadia Podoroska 6-3 6-2 to set up a meeting with Czech player Marie Bouzkova.

However, American Madison Keys survived a huge scare as the former finalist saved five match points to come through a thrilling match against Hungary's Anna Bondar.

After forcing a third set, Keys, the 22nd seed at her home slam, trailed the decider by a double break of serve.

She stayed alive after Bondar produced back-to-back double faults on her first two match points, and three more on her subsequent service game, before breaking again to level the set and eventually clinching a 10-point tie-break to win 5-7 6-4 7-6 (10-5).