Clijsters was not required to play in the first round.
The Belgian ranked 1st in the world beat Barbora Zahlavova Strycova (WTA 72) of the Czech Republic in two sets, 6-2 and 6-1. It was the first time the two players met.
In the next round, Clijsters meets Alisa Kleybanova (WTA 27) of Russia. Kleybanova earlier beat Tsvetana Pironkova (WTA 127) of Bulgaria 6-7, 6-3 and 6-1.
Earlier in the day another Belgian Yanina Wickmayer (WTA 15) also made her way through to the third round.
Belgium's number one beat Germany's Julie Görges 6-2 and 6-4. In the next round, Wickmayer plays Roberta Vinci of Italy.
The third Belgian, Kirsten Flipkens dismissed Canada's Aleksandra Wozniak (WTA 35) in two sets: 6-1 and 6-2. In the third round Flipkens plays Yelena Dementieva of Russia.