Venus Williams has moved within two wins of a possible sisterly showdown with Serena in the semi-finals of the US Open by beating German 26th seed Laura Siegemund to reach the fourth round.

The sixth-seeded Williams came up big on the critical points to make quick work of Siegemund in a 6-1 6-2 victory in Arthur Ashe Stadium.

The 36-year-old Williams, the oldest player in the women’s draw, repelled seven of nine break points held by the German, and capitalised on six of 10 of her own break opportunities.

“Just doing what I have to do, being able to dominate when I need to,” Williams told reporters.

“Being in control of the points, so even if I lose a point, I feel like, OK, I’m in a position to win the point. That’s where I want to be every single time.”

Williams, a seven-times grand slam singles winner and twice US Open champion, has enjoyed some recent success, reaching the semi-finals at Wimbledon and the final at Stanford.

As for her sister, that inflamed right shoulder that was supposed to hinder her as she seeks a record 23rd major title seems to be just fine.

“Definitely feels solid,” she said.

Not sure? There’s plenty of evidence. No need to take her word – or her coach’s – for it.

Look at the way Serena beat 47th-ranked Johanna Larsson 6-1 6-1 to reach the fourth round at Flushing Meadows and collect the 307th Grand Slam match victory of her career, surpassing Martina Navratilova for most by a woman in the Open era and equalling Roger Federer for most by anyone since 1968.

“Tennis-wise, I think it was very satisfying in all aspects. It’s not perfect, of course,” said her coach, Patrick Mouratoglou.

“But for someone who didn’t play much matches in the last two months, I think she’s competitive.”

Now there’s an understatement.

“There is no pain. Maybe she feels a little. But I see she plays normal. She serves normal. At practice, she serves the quantity that we usually do, full power,” Mouratoglou said.

“So I don’t see any problem.”

That sounds like bad news for upcoming opponents, starting with 52nd-ranked Yaroslava Shvedova, who advanced to the round of 16 in New York for the first time by beating Zhang Shuai 6-2 7-5.

Fifth-seeded Simona Halep smashed her racket in frustration en route to a 6-1 2-6 6-4 victory over 34th-ranked Timea Babos.

Carla Suarez Navarro defeated Elena Vesnina 6-4 6-3 to mark the third time she has reached the fourth round or better at Flushing Meadows.