Drago will next face Adam Duffy to continue his attempt to make it into the final stages of the tournament.
Young Belgian prospect Luca Brecel also made it through to the second round in style, thrashing Daniel Wells 5-1.
There was disappointment for China's Zhang Anda, however, who lost 5-3 to Rod Lawler to see his campaign come to a premature end.
Wuxi Classic qualifying first round results:
Thepchaiya Un-Nooh 5-2 Robbie Williams
Aditya Mehta 5-3 Sam Baird
Pankaj Advani 4-5 Chen Zhe
Tony Drago 5-1 Sean O'Sullivan
Luca Brecel 5-1 Daniel Wells
Hossein Vafaei Ayouri v Fraser Patrick w/o
Thanawat Tirapongpaiboon 5-3 Ian Burns
Zhang Anda 3-5 Rod Lawler
Tian Pengfei 5-4 Duane Jones
David Grace 2-5 Martin O'Donnell
Ben Judge 1-5 Adrian Gunnell
Michael Leslie 2-5 Paul Davison
Kurt Maflin 5-3 Jamie O'Neill
Cao Yupeng 4-5 Joel Walker
Liam Highfield 4-5 Michael Wasley
Craig Steadman 5-3 Michael Wild