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.

Wiltshire Conservatives call for urgent Government action over potential fire station closures
Nearly 100 arrested as South West police forces unite to tackle illegal drugs and child criminal exploitation
Rockbourne Fair celebrates another record-breaking year
Collaboration between Police and CCTV put prolific shoplifters behind bars
Tiny Titans Opening at Longleat for Easter
New Ways to 'Take Part' at Salisbury Arts Centre
Salisbury HGV driver urges others to quit this No Smoking Day
Tyre change excuse leads to £1,000 fly-tipping fine
