Thatcham won their Third Round tie at The Racecourse, defeating Berks County 3-1 in the first meeting between the two sides.
New signing Harvey Flippance scored either side of half-time, on both occasions converting after the home goalkeeper had saved shots from team-mates.
In the early stages Shamar Moore put Town ahead, latching on to a ball forward and lifting it over the keeper.
Ellis Day had levelled for County on 17 minutes, firing home the loose ball after it had come back off the woodwork.
Prior to the game Town had announced the short-term signing of veteran goalkeeper Paul Strudley, who last played for the club in 2020.
Teams that join Thatcham in the Fourth Round draw are Beaconsfield Town, Amersham Town, Aylesbury Vale Dynamos, Bracknell Town, Binfield, Flackwell Heath, Aylesbury United, Hungerford Town OR Slough Town, Ascot United OR Milton United.
MK Dons, Reading and Wycombe Wanderers will then join the Fourth Round winners in the Quarter Finals.
TEAM : Paul Strudley, Tinashe Gwavava, Callum Winchcombe, Callum Willmoth, Mo Ceesay, Andy Matthews, Zion Nditi, Roberto Nditi, Harvey Flippance, Shamar Moore, Kyle Daniel-Spray
ROLLING SUBS ON : Oli Bourne, Jenson Mansel, Kartel Forde, Harvey Fox, Harry Thorpe