Fifth seed Murphy, the 2005 15-reds world champion, disposed of second seed Trump while Davis, seeded 13th, was too good for Wuxi Classic winner Walden.
In the last eight, top seed Mark Selby – who had previously boasted a 100 per cent record at the tournament, which started with a group stage – lost a tight encounter 7-5 to Trump.
Murphy scraped through 7-6 against Welshman Dominic Dale, seeded 16, while Davis and Walden both eked out 7-5 victories against amateurs Panompai Powises and Issara Kachaiwong respectively.
Shaun Murphy 7-2 Judd Trump
Mark Davis 7-2 Ricky Walden
Shaun Murphy 7-6 Dominic Dale
Ricky Walden 7-5 Issara Kachaiwong
Mark Davis 7-5 Panompai Powises
Judd Trump 7-5 Mark Selby