Williams reached the last four of the Shanghai Masters ranking event the previous week, losing to runner-up Judd Trump in the semi-finals while Bingham made it to the quarters, with both receiving first-round walkovers in Yixing.
Williams defeated Ju Reti 4-0 while Bingham shut out Wong Yu Chen by the same score to reach Wednesday’s last-32 stage, where further local opposition awaits.
Former two-time World champion Williams will play Wang Linhan while Niu Zhuang awaits Wuxi Classic runner-up Bingham.
World number 37 Rory McLeod did not fare so well against unknown opposition, however, losing a final-frame decider 4-3 to Zhang Yang.
Ding Junhui, Mark Davis and Ricky Walden were also taken to a seventh frame, but were able to get past Oliver Brown, Liu Chuang and Yu Delu respectively.
Up next for Ding is Tang Jun while Walden will meet Tom Ford, who received a walkover against Andy Lee.
Other notable third round fixtures include Matthew Stevens v Liang Wenbo and Jamie Jones v Joe Perry.
Rounds three and four and the quarter-finals will be concluded on Wednesday, with the semi-finals and final on Thursday.
Asian PTC2 Round Two results
Stuart Bingham 4-0 Wong Yu Chen
Niu Zhuang 1-4 Cui Ming
Li Yan 4-2 Hu Hao
Michael Holt 2-4 Jin Long
Li Yuan 4-2 Hossein Vafaei Ayouri
Cao Yupeng 4-1 Xu Xinjian
Wang Linhan 4-1 Guan Zhen
Ju Reti 0-4 v Mark Williams
Ding Junhui 4-3 Oliver Brown
Pa Ruke 2-4 Tang Jun
Yu Delu 3-4 Ricky Walden
Tom Ford w/o Andy Lee
Cai Jianzhong 0-4 Liang Wenbo
Matthew Stevens 4-1 Lin Yongzhi
Marcus Campbell 4-1 Zhao Xintong
Zhou Yuelong 4-1 Zhang Anda
Chen Zhe 4-0 Wang Hen
Shi Hanqing 4-2 Li Yinjin
Rouzi Maimaiti 2-4 Barry Hawkins
Rory McLeod 3-4 Zhang Yang
Mei Xiwen 4-1 Paul Davison
Li Hang 2-4 Marco Fu
Cao Xin Long 4-2 Lu Ning
Xiao Guodong 4-3 Tian Pengfei
Ben Woollaston 4-2 Lu Haotian