Laverstock and Ford FC will face Bishops Cleeve in the first qualifying round of the FA Cup.
The 'Bulldogs' have already overcome Cowes Sports from the Isle of Wight and, at the weekend, beat local rivals Bemerton Heath Harlequins.
After going behind in the early stages to a Danny Young goal on 17 minutes, Laverstock fought back, and Carson Arnold levelled things up before the break.
Jake Watson put Laverstock in front with 15 minutes to play before Arnold grabbed his second of the game to seal a 3-1 victory over the higher-ranked side.
Like Harlequins, Bishops Cleeve ply their trade in the Southern League Division One South, a league higher than Laverstock. The Cheltenham-based side has yet to win a league game this season, but they beat Highworth Town and Lydney Town to reach this stage.
After winning their preliminary matches, Laverstock has already earned over £2500 in prize money, with more to come regardless of how they perform in their next match.