Number one seed Ash Barty shrugged off a blip deep in the second set to beat Clara Tauson and book her place in the third round of the US Open.
At a set and a break to the good, Barty looked on course to wrap up the contest in rapid fashion.
However, her Danish opponent broke back and Barty had to dig in to wrap up a 6-1 7-5 success.
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It was a surprise Barty was broken as she produced a powerful display on serve, sending down 11 aces.
Barty, who hit 33 winners in the match, will face tougher tasks as she closed out the match in an hour and 30 minutes.
Belinda Bencic was a semi-finalist at Flushing Meadows in 2019, and the Swiss served notice of her quality with a 6-3 6-1 win over Martina Trevisan.
Maria Sakkari broke serve on five occasions in her 6-4 6-2 win over Katerina Siniakova, Varvara Gracheva sent the 24th seed Paula Badosa packing with a 6-4 6-4 win – and Anett Kontaveit was a 6-4 6-1 victor over Jil Teichmann.
Number seven seed Iga Swiatek overcame the shock of losing the first set to claim a 3-6 7-6(3) 6-0 win over Fiona Ferro.
Petra Kvitova was made to battle in the first set before easing to a 7-6(4) 6-2 win over Kristyna Pliskova, while Anastasia Pavlyuchenkova needed three sets to overcome Anna Karolina Schmiedlova.
Angelique Kerber had no trouble in disposing of Anhelina Kalinina 6-3 6-2, while Jessica Pegula beat Misaki Doi by the same scoreline.
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Source: Euro Sports