The veteran world number 43 secured the first set with two late breaks, but then her Chinese Taipei opponent, ranked 303, responded to force a decider.
Stosur, though, closed out the match in just under two hours on Centre Court after a double break had seen the 33-year-old move 4-1 ahead.
Eighth seed Shuai Zhang, China's world number 31, breezed past Kurumi Nara of Japan 6-0 6-0 in just 50 minutes and Shelby Rogers is also through after the American defeated Su Jeong Jang of South Korea in straight sets, winning 6-4 6-4.
WTA Hong Kong
Pavlyuchenkova beats Gavrilova in Hong Kong final
15/10/2017 AT 18:46
American Nicole Gibbs is on course for a potential second-round contest against top seed Elina Svitolina, the world number four from Ukraine, following her 6-4 2-6 7-5 win over Greek qualifier Valentini Grammatikopoulou.
Monday's late matches saw 19-year-old Australian Lizette Cabrera beat Japanese player Shuko Aoyama 7-5 6-3 while world number 48 Qiang Wang of China defeated Kai-Chen Chang 6-3 6-0.
At the Tianjin Open, all of Monday's scheduled singles were cancelled because of persistent rain.
As part of some 16 matches now set for Tuesday, Italian Sara Errani will continue her comeback from a doping ban against Kateryna Kozlova of the Ukraine.
Tournament organisers also confirmed China Open winner Caroline Garcia, the world number nine, had withdrawn because of injury, meaning Romanian Irina Begu will now face wildcard Maria Sharapova in the first round.
WTA Hong Kong
Svitolina and Williams progress to second round of Hong Kong Open
10/10/2017 AT 15:02
WTA Hong Kong
Konta withdraws from Hong Kong Open with foot injury
03/10/2017 AT 11:33