Playing on the Louis Armstrong Stadium court, Halep won an opening-set tiebreak against Kazakhstan's Elena Rybakina 13-11.

Rybakina won set two, but the Romanian won the third to complete a 7-6, 4-6, 6-3 victory and advance to the last 16.

She will play Ukrainian fifth seed Elina Svitolina next, following Svitolina's 6-4, 6-2 win over Daria Kasatkina.

Svitolina needed just 74 minutes to beat the Russian.

In the biggest story of the day, Japan's Osaka lost to 18-year-old Leylah Fernandez of Canada.

Osaka served for the match in the second set, but capitulated under pressure, smashing her racket on numerous occasions, hitting a ball into the crowd and hiding under a towel as her play unravelled over the final two sets.

Fernandez eventually ran out a 5-7, 7-6, 6-4 victor, with Osaka - who dropped out of the French Open and skipped Wimbledon this year to deal with her mental health - revealing she will take an indefinite break from the sport.

Elsewhere at the Billie Jean King National Tennis Center, Germany's Angelique Kerber defeated American Sloane Stephens in a meeting of two former US Open champions.

Kerber - victorious in New York in 2016 - fought back to win 5-7, 6-2, 6-3.

The German will face defending champion Naomi Osaka next, should the Japanese player beat Canada's Laylah Fernandez later.

Spaniard Garbiñe Muguruza beat Belarus' Victoria Azarenka over three sets in a battle of two-time Grand Slam winners, and she will face Czech Barbora Krejčíková in round four.

Krejčíková has never before played in the singles main draw at the US Open but is enjoying a remarkable 2021, having won French Open singles and doubles titles, as well as the women's doubles gold medal at the Tokyo 2020 Olympics.

She beat 20-year-old Russian Kamilla Rakhimova in straight sets today.