The first-round match was played on Wednesday after rain wreaked havoc with the schedule.
The Russian's first-serve percentage was only 59 per cent, but she was able to overpower the Pole and saved nine break points to get the job done in two sets, setting up a meeting with Stefanie Voegele - who ousted Yulia Putintseva in the final match of the day.
Second seed Williams, playing in her second match since the US Open, lost 7-5 6-2 to the Japanese, who is ranked 64th in the world.
The five-time grand slam champion needed only an hour and four minutes to wrap up a 6-3 6-1 victory on Friday.
After rain interrupted the opening days of the tournament, Sharapova said: "It's been a long wait for everyone, it hasn't been easy".
Peng stayed in the hunt to retain her title on home soil with a brutal 6-0 6-1 demolition of Sara Sorribes Tormo.
Fifth seed Sorana Cirstea defeated Natalia Vikhlyantseva, 7-6 (14), 6-4, to make it to the quarterfinals of the Upper Austria Ladies' Linz for the first time in six years.
Aryna Sabalenka of Belarus is also through to the quarters, beating Zhu Lin of China 6-3 6-4.
The Pole had made it to the second round of the Tianjin Open following a victory over Ukraine's Kateryna Bondarenko. The Italian was banned after reportedly unknowingly ingesting letrozole, which was found in her mother's cancer medication.
Venus Williams was knocked out in the second round of the Hong Kong Open by 19-year-old Naomi Osaka.
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