Kim Clijsters, ranked third in the world, defeated Australia's Sally Peers 6-3, 6-1. Clijsters made 15 unforced errors in the first set before steadying to take the win over the number 201, who came through qualifying to gain entry to her first Grand Slam tournament.
"I had to find my feet again, in the wind it"s never easy. As the match went on I read her game better and played better myself. But I have a way to go to reach my best tennis," said Clijsters after the match.
"That takes time. I want to grow with every match, as the opponents get tougher I hope to play better," she added.
The Belgian second seed will play 27th seed Petra Kvitova of the Czech Republic for a place in the fourth round.