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Faversham booked an FA Trophy first round trip to Ryman League Premier Division side Kingstonian after recording a 2-1 preliminary round win at Walton & Hersham on Saturday.
Goals either side of the break from Dave Botterill and Damian Abel sent them through after the hosts had gone ahead inside two minutes.
Botterill's superb 30-yard free-kick found the top corner on the half hour and Botterill turned provider on 54 minutes, setting up Abel to score his third in three games since returning to the Lilywhites.
An under-strength Sittingbourne crashed out of the preliminary round, 2-0 at Arlesey Town.
After a goalless first half the Bedfordshire side scored twice after the break to sent Gary Abbott's side home empty-handed.
Whitstable Town put in a dismal display as they lost 2-0 at Ilford. Dan Wisker struck the woodwork after the interval as the visitors looked to break the deadlock but it was eventually the hosts who scored twice. To add insult to injury Ian Pulman missed a late penalty for the Oystermen.
Chatham Town went out 2-1 at Redbridge. After Chatham had struck the woodwork, the hosts took the lead in the 70th minute and doubled the advantage five minutes from time as Chatham pushed forward.
Joe Fuller (pictured) blasted in after a goalmouth melee on 88 minutes to set up a tense finale but the visitors could not find a leveller.
Thamesmead face a replay at Heybridge Swifts on Tuesday night after drawing 0-0 at Bayliss Avenue on Saturday.