World number one Victoria Azarenka continued her smooth progress though the US Open draw with a 6-2 6-2 victory over qualifier Kirsten Flipkens.
It was not quite as straightforward as the scoreline suggests, with many of the games close, but in the end Azarenka was too powerful and too consistent for her opponent.
A break in the third game of the match set Azarenka on her way and, although Belgian Flipkens briefly threatened a revival at the start of the second set, it was not to be.
Azarenka clenched her fist as she broke once more to lead 5-2 and then served out victory after an hour and five minutes.
The Belarusian is looking for her second grand slam title of the year after winning the Australian Open in January and she next faces Chinese 28th seed Zheng Jie, a 6-3 6-1 winner over Magdalena Rybarikova today.
Azarenka was happy to come through in windy conditions, saying: "I think it was another good performance today. It was a little bit difficult with the wind.
"I think I adjusted really well. Her game is also a little bit unpredictable. She likes to move the opponent around. She has different variety. It wasn't as easy maybe as the score was, but I think I played well."
American wild card Mallory Burdette continued her dream run with a 6-2 6-4 victory over Czech Lucie Hradecka. The 21-year-old studies psychology at Stanford and, as an amateur, cannot pick up the US dollars 65,000 cheque for reaching the third round.
Burdette is likely to meet third seed Maria Sharapova next, and she said: "I have already checked the amateur box so you can't go back once the tournament starts. It's done."
Czech Lucie Safarova, the 15th seed, was given a real test by Canada's Aleksandra Wozniak before prevailing 6-3 4-6 6-2 while Nadia Petrova and Varvara Lepchenko are also through.