The Hellenic Football League side overcame Fleet Spurs 4-2 after extra-time in their First Qualifying Round replay, despite being a goal down at half-time.
In an end to end encounter, New College Swindon fought back during the second-half with goals from Christy Millar and Max Slinn forcing an addition 30 minutes of play.
The FA Carlsberg Vase
First Round Qualifying Replays
Tuesday 9 September 2014
Winning clubs each receive £600 from The FA's Prize Fund
By Simon Collings
And it was the same duo who proved to be the difference during extra-time as both Millar and Slinn once again found the net to secure a memorable victory for their club.
Of the eight replays which took place on Tuesday, there was only one other that went to extra-time - that being the tie between Bromsgrove Sporting and Stourport Swifts.
Unlike in New College Swindon’s match, it was the home team who were left celebrating as Bromsgrove defeated their opponents 3-2 after extra-time.
Bromsgrove could have been in the hat for the next round sooner, but a 90th minute equaliser from Stourport made it 2-2 at the end of normal time.
However, Bromsgrove managed to regain their composure and secure victory thanks to Simon Fitter’s goal just seven minutes from time.
Bromsgrove’s home win was one of six on the night, with just two teams managing to record victories away from home, Potton United the only other victors on their travels.
The Counties League Division One team came from a goal behind to defeat Winslow United 2-1, scoring a 90th minute winner to the delight of the travelling fans who had made the trip.