Errani won the first set 6-0 before dropping the second 6-3 to her unseeded opponent.
But the Italian hit back to take the final set 7/3 in a tie-break.
Czech third seed Klara Zakopalova had much easier progress as she beat Croatia's Donna Vekic 6-3 7-5.
There was an upset as Serbian fourth seed Bojana Jovanovski lost 6-1 7-5 to Germany's Anna-Lena Friedsam.
Seventh seed and home favourite Zheng Jie defeated Israel's Shahar Peer 6-0 6-3.
There were also wins for Germany's Annika Beck, Austria's Patricia Mayr-Achleitner, Slovakian Jana Cepelova, Switzerland's Viktorija Golubic, Vania King of the United States and the Czech Republic's Barbora Zahlavova Strycova.