It was a desperate day for legend Davis, who was comprehensively thrashed 5-0 by Michael Wild.
The veteran former world champion could not find any rhythm in the match as Wild swept to a convincing win with consummate ease.
And fellow veteran White withdrew from the qualifiers to hand his opponent Liam Highfield a walkover into the next round.
Cao Yupeng continued his impressive run as he beat Mike Dunn 5-2 in the third round.
The Chinese player, whose victory over Mark Allen at the World Snooker Championships in the Steel City last month led to the Northern Irishman picking up a £10,000 fine for branding Yupeng a “cheat”, thrived in his third-round encounter.
Dunn could only muster two frames in response as Yupeng stormed through to the next round with real confidence after an emphatic win.
Matthew Selt overcame a tough resistance from Thepchaiya Un-Nooh to win their third-round match 5-3.
Selt started the match brilliantly, but Un-Nooh responded to ensure a hard-fought encounter.
But the Romford man hit back once more to take victory and seal his progression.
Michael White was another winner on Thursday as he comfortably disposed of Mitchell Mann with a 5-2 victory.
Xiao Guodong was victorious in his match against Kurt Maflin, taking it 5-4; meanwhile, Thanawat Tirapongpaiboon beat Peter Lines by the same scoreline.
In the afternoon session, nip-and-tuck clashes saw Dave Harold edge Sam Baird and James Wattana shade Jimmy Robertson, both by 5-4 margins.
In the evening session, Alan McManus brought Tony Drago's run to an end with a narrow 5-4 win while Ben Woollaston was bounced out 5-1 by Barry Pinches.
Liu Chuang advanced to the final round of qualifying with a 5-2 win over Pankaj Advani and there were also victories for Gerard Greene and David Gilbert.
Round three results:
Matthew Selt 5-3 Thepchaiya Un-Nooh
Michael White 5-2 Mitchell Mann
Xiao Guodong 5-4 Kurt Maflin
Peter Lines 4-5 Thanawat Tirapongpaiboon
Steve Davis 0-5 Michael Wild
Mike Dunn 2-5 Cao Yupeng
Dave Harold 5-4 Sam Baird
Nigel Bond 5-2 Michael Wasley
Anthony McGill 5-3 Dechewat Poomjaeng
Jimmy Robertson 4-5 James Wattana
Jimmy White v Liam Highfield w/o
Alan McManus 5-4 Tony Drago
Ben Woollaston 1-5 Barry Pinches
Liu Chuang 5-2 Pankaj Advani
Gerard Greene 5-3 Rod Lawler
David Gilbert 5-0 Martin O'Donnell