The Chinese star overcame five double faults and struggled with her serve during the 94-minute match.
Li will play eighth-seeded Bojana Jovanovski of Serbia.
No. 2-seeded Marion Bartoli also advanced by defeating Swiss qualifier Stefanie Voegele 7-5, 6-4. Bartoli will take on fifth-seeded Klara Zakopalova of the Czech Republic for a place in the semifinals.
China's Zhou Yi-miao, ranked 177, completed the quarterfinals lineup with a 4-6, 6-2, 7-6 (3) win over Taiwan's Chang Kai-chen. Romania's Monica Niculescu, who ousted No. 7-seeded Laura Robson in the first round, will take on Zhou on Thursday.