Defending US Open champion Sam Stosur set up a fourth-round meeting with Britain's Laura Robson by beating Varvara Lepchenko in straight sets.
The Australian, seeded seventh, won a first-set tie-break before wrapping up a 7-6 (7-5) 6-2 victory in one hour and 28 minutes.
World number one Victoria Azarenka looked imperious as she defeated Zheng Jie 6-0 6-1 in 59 minutes.
French Open champion Maria Sharapova beat American Mallory Burdette 6-1 6-1.
And Petra Kvitova, the 2011 Wimbledon champion, earned a 6-4 6-4 win over France's Pauline Parmentier.
Stosur, who has not won a title of any description since beating Serena Williams in the final at Flushing Meadows last year, admitted that it took her a while to find her rhythm against Uzbekistan-born American Lepchenko.
She said: "I think once I got that first set then I maybe relaxed a little bit more.
"Once I got that break and then started to maybe see what was going on a bit more, it became a little bit easier for me."
Top seed Azarenka, who has lost six games in her first three matches at Flushing Meadows, will play Anna Tatishvili for a place in the quarter-finals.
The Belarusian lost merely seven points in the first set and thanked the New York fans for their support.
"I think you guys inspired me to play my best tennis. It's an incredible atmosphere and energy," said the Australian Open champion.
"I always wanted to play here, I've watched on TV but it felt really different. It was amazing."
Czech number five seed Kvitova's victory over Parmentier set up a meeting with Marion Bartoli.
Bartoli, the number 11 seed, beat fellow Frenchwoman Kristina Mladenovic 6-2 6-4.
Sharapova, the number three seed, took just 58 minutes to see off world number 252 Burdette.
The Russian said: "She's got a big solid game from the back and I wanted to take that away from her.
"Of course I would have loved to have served a little better in that second set. I gave her that break but overall it was pretty solid. Considering the conditions, I thought I served good and placed the ball well."