Williams beat fellow American Vania King 6-3 6-3 to reach the third round of the US Open and tie the record.

Hitting 13 aces with the roof closed at Arthur Ashe Stadium, Williams improved to 306-42 in matches at major tournaments and in doing so went closer to the all-time record for matches won at grand slams.

Only Roger Federer, with 307, has won more grand slam matches than Williams in the Open era, which dates back to 1968.

Williams can match Federer’s total by beating 47th-ranked Johanna Larsson of Sweden, who she will play in the third round. Equally impressive was her older sister Venus, who stayed on track for a possible semi-final clash with Serena by sprinting past German Julia Goerges to reach the third round.

Venus, 36, relied on her big serve throughout the match, posting a 6-2 6-3 victory over the German.

Venus Williams, the US Open winner of 2000 and 2001, was runner-up to top seed Martina Hingis as an unseeded player in the inaugural year of Ashe Stadium and 19 years later finished the first US Open day session played entirely under a roof.

“1997 was a long time ago,” Williams said on court after her victory.

“I’m so grateful to be here still playing, still winning matches and I can’t wait for the next round.”

The elder Williams sister will next play either 26th seed Laura Siegemund of Germany or American Nicole Gibbs.

Earlier on day three Romanian fifth seed Simona Halep advanced to the third round with a 6-3 6-4 win over Lucie Safarova in the first full match played under a closed roof at Arthur Ashe Stadium.

“It was a little bit (of an adjustment),” Halep said about playing under the roof.

“But I had the chance to warm up in the morning before the match.

“I don’t want to say anything bad because it wasn’t bad. Had a nice feeling.

Halep will play Hungary’s Timea Babos in the third round.

Also advancing to the third round is Polish fourth seed Agnieszka Radwanska, who beat Briton Naomi Broady 7-6 (11-9) 6-3.

Radwanska will now face French 25th seed Caroline Garcia.