Dominic Thiem dispatched Félix Auger-Aliassime in little more than two hours ©Getty Images

Serena Williams and Dominic Thiem both advanced to the quarter-finals of the US Open as the tournament in New York City entered its second week.

American Williams, who is attempting to win a record-equalling 24th Grand Slam singles title, was up against Maria Sakkari of Greece.

Sakkari defeated Williams at the Cinicinnati Masters - also played at the Billie Jean King National Tennis Center in New York - last month.

Williams won the first set 6-3, but Sakkari held her nerve to win the second via a tiebreak and set up a decisive third set.

However, with Williams up 4-3, Sakkari gave up a soft break and ultimately fell to a 6-3, 6-7 (6-8), 6-3 defeat.

"She was doing so well," Williams said of her opponent after the match.

"She was being so aggressive and I knew I needed to do the same thing."

Sakkari in turn rued not being more aggressive in the third set, but reaching the fourth round ties her career-best performance at a Grand Slam after she alose reached this stage of the Australian Open earlier in the year.

Serena Williams has now won back-to-back three-set matches ©Getty Images
Serena Williams has now won back-to-back three-set matches ©Getty Images

Williams will face Tsvetana Pironkova of Bulgaria in the last eight, who is remarkably through to the quarter-finals despite having not played in a tournament for more than three years.

Wimbledon in 2017 was Pironkova's last tournament and she had time off after giving birth to a son, but has been in brilliant form in Flushing Meadows and the set she dropped today against Alizé Cornet is the first she has lost this tournament.

Pironkova beat the Frenchwoman 6-4, 6-7 (5-7), 6-3.

In the men's draw, number two seed Thiem produced a clinical display to beat 20-year-old Canadian Félix Auger-Aliassime 7-6 (7-4), 6-1, 6-1.

Austria's Thiem needed two hours and seven minutes to reach the quarter-finals, where Alex de Minaur awaits.

Thiem has never been beyond the US Open quarter-finals, but is a three-time Grand Slam runner-up and the top seed left in the men's singles contest.

Australian De Minaur, who at 21 has never before gone this deep at a Grand Slam, also beat a Canadian.

He brushed aside Vasek Pospisil 7-6 (8-6), 6-3, 6-2.

Two last-eight spots remain in both the men's and women's contests, with American number two seed Sofia Kenin and Russian Daniil Medvedev - last year's runner up and the men's number three seed - both in action in the evening session.