King brushed aside Robbie Williams 6-3 in a commanding performance in the afternoon session, and the world number 35 always looked like progressing.
Liang had a slightly tougher encounter as he battled past Adam Duffy with a 6-4 win to seal his place in the next round.
The Chinese player, who is ranked at number 39 in the world, had just too much for Duffy, who was unable to build on a number of promising breaks.
It was not a good day for world number 40 Rory McLeod or Jimmy White, however, who suffered defeats to David Gilbert and Aditya Mehta, respectively.
Michael White 6-2 Thepchaiya Un-Nooh
Ben Woollaston 3-6 Paul Davison
Jamie Jones 2-6 Liu Chuang
Anthony Hamilton 6-3 Luca Brecel
Rory McLeod 3-6 David Gilbert
Alan McManus 3-6 Pankaj Advani
Gerard Greene 5-6 Alfie Burden
Jack Lisowski 2-6 Kurt Maflin
Mark King 6-3 Robbie Williams
Jimmy White 5-6 Aditya Mehta
Liang Wenbo 6-4 Adam Duffy