• Federer improves to beat Feliciano López in straight sets • Nadal rallies from a set down against Leonardo Mayer

This article is more than 3 years old

This article is more than 3 years old

Roger Federer and Rafael Nadal continued their progress towards a potential US Open semi-final meeting on Saturday, with both players winning their third-round matches to progress to the last 16.

After two five-set marathons Federer had the afterburners on, sprinting past the Spaniard Feliciano López 6-3, 6-3, 7-5 in just 1hr 46min under a closed roof at Arthur Ashe Stadium.

In his opening two matches at Flushing Meadows a misfiring Federer had been forced to five sets, first by the American young gun Frances Tiafoe then the Russian veteran Mikhail Youzhny. After being broken eight times and committing 124 unforced errors in those first two contests, a focused Federer tightened up his game against the No31 seed López, operating with his trademark efficiency.

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Federer hit 32 winners and just 16 unforced errors against López, breaking in the sixth game and clinching the opening set in just 25 minutes. The six-times US Open champion’s only blip came in the third set when his opponent broke back – but Federer broke in the 12th game of the set to close out the match and set up a meeting with Germany’s Philipp Kohlschreiber.

“It was clearly nice to go up two sets to love for a change,” Federer said with a smile.

“I was happy I had good energy because I think that was my biggest worry, that somehow after the two five-setters that I was going to feel a little slow, hard to throw the engine on, that I would have to force myself so much, I would get tired from that. It didn’t happen.

“I’m really pleased with the performance. It’s exactly I guess maybe what I needed going into the next round.”

The world No1 Nadal did not find things quite so straightforward against Leonardo Mayer. Nadal lost the first set in a tie-break but battled back to win 6-7(3), 6-3, 6-1, 6-4 and will face Ukraine’s Alexandr Dolgopolov in the fourth round.

Mayer played neat and powerful shots to stave off six break points in the first set and force a tie-break. The unseeded Argentinian took a mini-break when Nadal inexplicably hit a routine backhand into the net and then sealed the set with an unreturnable serve.

Facing two break points in the fourth game of the second set, Nadal produced two massive shots to swing the match back in his favour, and broke Mayer to move ahead in the next game. The Spaniard went on to win seven successive points and took the second set with a jaw-dropping passing shot.

Normal service had resumed as Nadal won his seventh successive game to open up a 3-0 lead in the third set. Mayer briefly threatened a comeback when he pulled a break back for 5-3 in the fourth set but Nadal served it out after Mayer sent a forehand long.

“It was a tough situation for a set and I had some break points against me early in the second,” Nadal said. “I fought, I was there mentally and then I started to play much better.

“I must improve on the forehand. At the end of the match I was creating more space but at the beginning I failed to convert several chances.”

Keys joins home hopefuls in last 16

In the later match at Arthur Ashe Stadium, Madison Keys claimed a 2-6, 6-4, 6-1 win against the Russian Elena Vesnina, in a match that ran into the early hours of Sunday morning.

The No15 seed Keys recovered from a dreadful start to set up a fourth-round meeting with Elina Svitolina, in a match that finished at 1.46am local time.

Facebook Twitter Pinterest Madison Keys celebrates her late victory over Elena Vesnina. Photograph: Julio Cortez/AP

Svitolina downed the local favourite Shelby Rogers 6-4, 7-5 but there will still be five Americans in the women’s last 16, with Venus Williams, Sloane Stephens, Jennifer Brady and CoCo Vandeweghe also through.

Brady battled to a 6-3, 4-6, 7-6(3) defeat of Monica Niculescu, while Vandeweghe beat the 10th seed Agnieszka Radwanska 7-5, 4-6, 6-4.

“You guys were amazing, I definitely did not show up very well for the first set but you helped me get back into the match, thank you for helping me through that one,” Keys told the crowd.

“I think I finally settled in after being a bit over-amped at the start. Who doesn’t love a late show?”