Li, ranked No. 7 in the world, broke Minella four times without facing a break point. Next up for the Chinese star, trying to win her first title on home soil since 2004, will be Julia Cohen of the United States in the second round.
It was a good day for Chinese. Sixth-seeded Peng Shuai, chasing her first WTA singles title, swept past Ayumi Morita of Japan for a seventh straight time, 6-1, 6-1, and Zhou Yi-miao, a lucky loser who made the draw when third-seeded Jelena Jankovic withdrew, defeated American qualifier Jessica Pegula 6-4, 6-2.
Peng's win set up a quarterfinal with Annika Beck of Germany, who beat fourth-seeded Hsieh Su-wei of Taiwan 6-3, 6-0 in their first meeting.
Also through to the last eight were Monica Niculescu of Romania, who topped seventh-seeded Laura Robson of Britain 6-2, 6-3; fifth-seeded Klara Zakopalova of the Czech Republic; and eighth-seeded Bojana Jovanovski of Serbia, who awaited Li or Cohen.