World number 22 Day was whitewashed by Michael Wasley while no.23 Fu was edged out 4-3 by 22-year-old amateur Ryan Causton.
Liam Highfield beat Chinese Liang Wenbo 4-2.
In the second-round matches, 2002 world champion Peter Ebdon lost 4-3 to world no.68 Kurt Maflin.
Six-times world champion Davis, who beat John Whitty and former world number three James Wattana in rounds one and two, was too good for 14th-ranked Matthews Stevens in round three, winning 4-1.
Davis is currently ranked in 50th.
The tournament, known as the Kay Suzanne Memorial Trophy, runs from Sunday until Wednesday at the South West Snooker Academy in Gloucester.
RESULTS:
Round 3
Tony Drago 4-1 Jack Lisowski
Mark Selby 4-0 Chen Zhe
Steve Davis 4-1 Matthew Stevens
Barry Hawkins 4-0 Jimmy Robertson
Allan Taylor 3-4 Ian Burns
Ben Woollaston 3-4 John Higgins
Andrew Higginson 3-4 Anthony Hamilton
Michael Wasley 4-3 Kurt Maflin
Round 2
Tony Drago 4-2 David Grace
Jack Lisowski 4-2 Liam Highfield
Mark Selby 4-0 Alfie Burden
Chen Zhe 4-3 Dave Harold
Rory McLeod 2-4 Andrew Higginson
Ryan Causton 0-4 Anthony Hamilton
Liu Chuang 1-4 Michael Wasley
Allan Taylor 4-1 Jamie Cope
Barry Hawkins 4-1 Mark King
Peter Ebdon 3-4 Kurt Maflin
Robert Milkins 0-4 Ben Woollaston
Xiao Guodong 3-4 Ian Burns
John Higgins 4-2 Rod Lawler
Jimmy Robertson 4-3 Joe Perry
Steve Davis 4-2James Wattana
Martin Gould 2-4 Matthew Stevens
Round 1
Alfie Burden 4-0 Adam Edge
Chris Norbury 2-4 Chen Zhe
Dave Harold 4-2 Shane Castle
Andrew Norman 1-4 Tony Drago
David Grace 4-3 David Gilbert
Jack Lisowski 4-1 Fraser Patrick
Liang Wenbo 2-4 Liam Highfield
Robert Milkins 4-3 Mike Dunn
Rory McLeod 4-1 Michael Wild
Andrew Higginson 4-0 George Marter
Marco Fu 3-4 Ryan Causton
Anthony Hamilton 4-3 Oliver Brown
Pankaj Advani 2-4 Liu Chuang
Ryan Day 0-4 Michael Wasley
Jamie Burnett 1-4 Peter Ebdon
Kurt Maflin 4-2 Daniel Wells
Mark Selby 4-1 Anthony McGill
Allan Taylor 4-0 Zak Surety
Jamie Cope 4-2 Gareth Allen
Xiao Guodong 4-1 Jak Jones
Ian Burns 4-2 Adam Duffy
Barry Hawkins 4-2 Andy Hicks
Mark King 4-0 Aditya Mehta
Steve Davis 4-3 John Whitty
Luca Brecel 3-4 Jimmy Robertson
Joe Perry 4-2 Justin Astley
Ben Woollaston 4-0 James Cahill
John Higgins 4-1 Jamie O'Neill
Rod Lawler 4-0 Li Yan
James Wattana 4-2 Marcus Campbell
Martin Gould 4-1 Sam Baird
Joe Swail 0-4 Matthew Stevens
TUESDAY MATCHES (evening matches to be decided)
Mark Allen v Adam Wicheard
Paul Davison v Scott Donaldson
Dominic Dale v Joel Walker
Mark Joyce v Ben Jones
Ricky Walden v Joe O'Connor
Dechawat Poomjaeng v Dylan Mitchell
Stuart Bingham v Gerard Greene
Mark Williams v Zhang Anda
Michael Holt v Francisco Domingues
Yu Delu v Michael Leslie
Tian Pengfei v Barry Pinches
Alan McManus v Thanawat Tirapongpaiboon
Jimmy White v Ian Glover
Thepchaiya Un-Nooh v Sean O'Sullivan
Simon Bedford v Nigel Bond
Ding Junhui v Elliott Slessor
Fergal O'Brien w/o Ronnie O'Sullivan
Ken Doherty v Stuart Carrington
Graeme Dott v Matthew Selt
Craig Steadman v Kamal Chawla
Ali Carter v James Gillespie
Shaun Murphy v Kishan Hirani
Gary Wilson v Passakorn Suwannawat
Mark Davis v Matthew Day
Judd Trump v Martin O'Donnell
Peter Lines w/o Stephen Lee
Michael White v Darren Bond
Robbie Williams v Duane Jones
Jamie Jones v Callum Downing
Tom Ford v Kyren Wilson
John Astley v Ben Judge
Stephen Maguire v Cao Yupeng
