The 2011 French Open champion was not in vintage form in the first set, serving four double faults and making 21 unforced errors.
It was her ability to win crucial points that saw her edge in front, taking the first set 6-4.
However, the Romanian was completely overwhelmed in the second set and was unable to cope with the power coming from the opposite baseline.
Li served for the match at 5-0, but Cirstea managed to avoid a whitewash.
The end was not long in coming, though, as the 30-year-old wrapped up victory by breaking her opponent for the seventh time in the match.
She now faces a fourth-round clash with Julia Goerges, who overcame Zheng Jie 6-3 1-6 7-5.