American qualifier Taylor Townsend dumps Simona Halep out of US Open

Halep revealed: "After we played together, she came in the locker room and she asked me what she has to improve to be better. Next time I will not say anything."

Townsend, who will face Sorana Cîrstea in round three, recalled: "I don't know why I did it, but I did it. It kind of stuck with me.

"I'm not saying that everything she said I implemented into my training, but it was definitely in the back of my head to remember what she said and also remember why I asked, what drove me to ask that question, kind of that hunger and desire to get better."

Naomi Osaka is over her first-night nerves as her bid to defend her title gathers pace.

Osaka needed three sets to dispatch Anna Blinkova in her first-round match, but there was no such drama in her 6-2 6-4 win over Magda Linette.

"For me, going into this match I was very calm, because I was thinking there is no way my nerves could be worse than they were the day before," she said.

"For me, I also had that comfort of knowing I have played Magda before. I'd never played Blinkova before, so there is also that added stress not knowing what she can do.

"For me, that stress was taken away today. I came in pretty confident with my abilities and I think that showed a little bit."

Two-time Wimbledon champion Petra Kvitova was another surprise second-round casualty, the sixth seed losing 6-4 6-4 to Andrea Petkovic.

"I think that she likes my game, to be honest," said the Czech. "She played great. She moved pretty well as well.

"I had my chances, but I was always missing the last things. I was a break up in the second, and I should make it.

"But, yeah, overall I don't think I really played that bad. That's how it is. I was really trying hard. I was fighting."

Teenage wild card Coco Gauff is through after a 6-2 4-6 6-4 win over Hungarian qualifier Timea Babos.