Former world number two Knowles, 57, dropped to a 5-2 defeat at the World Snooker Academy to end his hopes of another run at the Crucible. He was a semi-finalist there on three occasions during the 1980s.
Astley moves onto a meeting with Paul Wykes, who beat Robin Hull 5-2.
Joe Swail, known as somewhat of a Crucible specialist, also won through to the next round after a 5-1 victory over David Morris.
The Northern Irishman has reached the World Championship semis twice - in 2000 and 2001 - and that last 16 a further four times. His qualification bid continues with a last-eight match against Stephen Rowlings, a 5-4 winner over Barry Stark.
Pre-qualifying round one results:
Ali Bassiri 0-5 Surinder Gill
Del Smith 4-5 Barry Stark
Paul Wykes 5-2 Robin Hull
Stephen Ormerod 5-0 Bill Kelly
Pre-qualifying round two results:
Andrew Norman 5-1 Philip Minchin
Les Dodd 5-4 Surinder Gill
David Morris 1-5 Joe Swail
Stephen Rowlings 5-4 Barry Stark
Justin Astley 5-2 Tony Knowles
Lucky Vatnani 3-5 Paul Wykes
David Singh 2-5 Tony Chappel
Patrick Wallace 5-0 Stephen Ormerod
Pre-qualifying quarter-finals match-ups:
Joe Swail v Stephen Rowlings
Andrew Norman v Les Dodd
Justin Astley v Paul Wykes
Tony Chappel v Patrick Wallace