Hawks keep their survival hopes alive... Gosport beaten
The Westleigh Park side remain in the bottom three but have a game in hand on the two clubs above them.
Swallow struck after 10 minutes to set the visitors on their way to only their second away win of the season.
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Hide AdGosport Borough slumped to a 3-0 defeat at Eastbourne Borough, with all the goals coming in the second half.
Bognor were pipped to the Ryman League title despite thumping Hendon 4-0 at Nyewood Lane.
The Rocks had to settle for a place in the play-offs after Hampton & Richmond won the league with a 0-0 home draw against Enfield.
Petersfield Town ended their Southern League division one central campaign with a 1-0 home defeat against Kings Langley.
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Hide AdIn the Wessex League, Moneyfields chalked up their second win in 24 hours by beating Fawley 2-1 on the Waterside.
Horndean thumped Bournemouth Poppies 6-1 at Five Heads Park, but Fareham Town had to settle for a 1-1 home draw against Whitchurch United.