China's No.1 got an early break against her 27th ranked opponent to go 2-1 ahead and was cruising at 4-1 before she was broken, reports Xinhua.
The former French Open winner responded by stepping up to break again but her service game let her down once before she cut down the error rate to take the set.
The Romanian crumbled in the second set, with Li racing through it in just 28 minutes to stay on track to meet German Julia Goerges, who beat Zheng Jie 6-3, 1-6, 7-5 earlier Friday.
It is the consecutive fourth time she has reached the fourth round at the Australian Open.