Jason Kite scored a brace for The Swan as they pulled off a shock 3-2 win at Banbury District & Lord Jersey League Premier Division Barford United.
An upset was on the cards as Kite's double and a Sam Kempsall strike gave Swan a 3-0 half-time lead.
After the break, James Castle and Shaun Wilson replied for Barford, but the Division 2 side held on to book their place in the second round.
In the league, Bishops Itchington eased to a 3-0 success against Bodicote Sports.
Jordan Cox fired them ahead on 25 minutes, before Steve Giggs made it 2-0 with a 20-yard shot which took a slight deflection on its way to the net.
Joe French scored No 3.
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