ImagoFormer world number two White benefited from a walkover in his scheduled second round match against Mohamed Khairy before he stepped up to the table to beat Andrew Norman 4-3 at the World Snooker Academy.
White's victory sees him progress into the round of 32, which will played in Gdynia, Poland from October 5-7.
Among those to book join him in booking tickets to Poland were Stephen Maguire, Joe Perry, Liang Wenbo and Neil Robertson.
But Davis was bounced out 4-1 by Jamie Jones and Drago lost 4-2 to Stuart Bingham to end their hopes of reaching Gdynia.
The second half of the draw play on Saturday to determine the remaining 16 places for October's tournament.
Round three results:
Stephen Maguire 4-0 Peter Lines
Jimmy Robertson 3-4 Michael Wasley
Xiao Guodong 0-4 Joe Perry
Robbie Williams 1-4 Mark Davis
Andy Hicks 4-3 David Gilbert
Liang Wenbo 4-1 Mark Allen
Zhang Anda 2-4 Dave Harold
Jimmy White 4-3 Andrew Norman
Anthony McGill 4-2 Matthew Day
Tian Pengfei 4-2 Pankaj Advani
Allan Taylor 3-1 Cao Yupeng
Tony Drago 2-4 Stuart Bingham
Ben Woollaston 4-3 Paul Davison
Martin Gould 4-0 Barry Pinches
Yu Delu 3-4 Neil Robertson
Jamie Jones 4-1 Steve Davis
Round two results:
Stephen Maguire 4-0 Simon Bedford
Peter Lines 4-0 Phil O'Kane
Jimmy Robertson 4-1 Adam Wicheard
Joel Walker 2-4 Michael Wasley
Xiao Guodong 4-3 Mark King
Joe Perry 4-2 Ashley Carty
Robbie Williams 4-2 Ben Harrison
Jamie Cope 3-4 Mark Davis
Andy Hicks 4-3 Oliver Lines
Matthew Couch 0-4 David Gilbert
Liang Wenbo 4-2 Liam Monk
Anthony Hamilton 2-4 Mark Allen
Liu Chuang 0-4 Zhang Anda
Dave Harold 4-1 Reanne Evans
Jimmy White w/o Mohamed Khairy
Andrew Norman 4-3 Jamie O'Neill
Anthony McGill 4-1 Adrian Gunnell
Jak Jones 1-4 Matthew Day
Ian Burns 2-4 Tian Pengfei
Pankaj Adani 4-3 Daniel Wells
Allan Taylor w/o Hossein Vafaei Ayouri
Cao Yupeng 4-2 Chen Zhe
Li Yan 3-4 Tony Drago
Stuart Bingham 4-0 Marc Davis
Ben Woollaston 4-0 Grzegorz Biernadski
Paul Davison 4-3 John Astley
Ricky Walden 2-4 Martin Gould
Thanawat Tirapongpaiboon 0-4 Barry Pinches
Yu Delu 4-1 Aditya Mehta
Neil Robertson 4-0 Alex Taubman
Barry Hawkins 1-4 Jamie Jones
Steve Davis 4-0 Wiktor Rzezuchowski
