Li, seeded seventh in her home country, moved on with a 6-2, 6-3 victory over an unseeded Italian Francesca Schiavone.
Both Li and Schiavone are former French Open winners.
Meanwhile, No. 6 seed Errani -- this year's second-place finisher in Paris -- was leading fellow Italian Camila Giorgi 5-4 in the first set when she retired with a thigh injury.
Among the other Day 2 winners were ninth-seeded Marion Bartoli of France, who dispatched Serbian qualifier Bojana Jovanovski 6-3, 6-3, and 18-year-old British qualifier Laura Robson, who dumped Japanese veteran Kimiko Date-Krumm, 6-4, 6-4.
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