Top seed Selby also made it safely through in the morning with a 4-1 win over Kyren Wilson and was even more clinical against King later on Saturday in his last 16 clash.
Jack Lisowski beat Scottish veteran Alan McManus in the last 32, but then went down to Rod Lawler 5-1 in his last 16 showdown.
The 21-year-old had edged 41-year-old McManus in the deciding frame to win 4-3 and earn a last 16 clash against Lawler, who was awarded a walk-over against Ken Doherty.
Doherty pulled out of the event in order to play some exhibition matches in China.
Mark Davis also made the last 16 with a 4-1 win over Liu Chang, and will face Tian Pengfei for a quarter-final spot.
Most of the last 16 matches were played on Friday.
Last 16 results:
Jack Lisowski 1-4 Rod Lawler
Mark Selby 4-0 Mark King
Last 32 results:
Played Saturday
Mark Selby 4-1 Kyren Wilson
Jack Lisowski 4-3 Alan McManus
Mark Davis 4-1 Liu Chuang
Ben Woollaston 4-2 Anthony Hamilton
Tian Pengfei 4-1 Mark Davis
Kurt Maflin 4-1 Liam Highfield
Dave Harold 0-4 Martin Gould
Played Friday
Thepchaiya Un-Nooh 1-4 Ian Burns
Jimmy Robertson 3-4 Dave Harold
Ricky Walden 1-4 Thanawat Tirapongpaiboon
Liang Wenbo 4-2 Justin Astley
Graeme Dott 4-2 Aditya Mehta
Tian Pengfei 4-0 Jamie Burnett
Matthew Stevens 0-4 Ben Woollaston
Stephen Maguire 2-4 Anthony Hamilton
Dominic Dale 2-4 Liam Highfield
Martin Gould 4-3 Rob Milkins
Neil Robertson 3-4 Kurt Maflin
Mark Davis 4-1 Liu Chuang
Ken Doherty v Rod Lawler w/o
