US Open 2019: All the major results from Day 3

16-time Grand Slam winner Djokovic overcame Argentina's 56th-ranked Juan Ignacio Londero 6-4, 7-6 (7/3), 6-1 in a testing affair.

"It was definitely affecting my serve and backhand. I was definitely tested," Djokovic said of his shoulder injury.

Djokovic will next come up against Dusan Lajovic or Denis Kudla.

"It's not the first time I'm facing this kind of adversity or challenge," he added.

After passing a stiff test against India's Sumit Nagal, 20-time Grand Slam winner Federer beat 99th-ranked Bosnian Damir Dzumhur 3-6, 6-2, 6-3, 6-4.

He had 17 unforced errors in the first set.

"When it happens like this, back-to-back matches, it's just a bit frustrating more than anything, especially when the level is that low and there is that many errors," he said.

Japanese star Kei Nishikori beat 108th-ranked American Bradley Klahn 6-2, 4-6, 6-3, 7-5.

Nishikori stumbled after seizing a 5-1 edge in the final set and needed five match points to win.

"A little bit of lost focus after 5-1. He started playing better too," he said.

Meanwhile, Grigor Dimitrov received a walkover from Borna Coric to progress.

Svitolina showed her prowess after edging past Venus in a 6-4, 6-4 affair at the Flushing Meadows.

She will now face Rebecca Peterson of Sweden or compatriot and 32nd seed Dayana Yastremska.

"It was an incredible match. We saw it was incredibly tough and only a few points divided the match," said Svitolina after her victory.