Substitute Marcus Robertshaw scored a late winner as Storrington gained some revenge over Mile Oak for two defeats earlier in the season
Swans Matt Chester had to make a couple of early saves before the visitors when ahead with a fine solo goal after 38 minutes, Joe Warner controlling well and beating a defender before calmly lobbing the Oak keeper.
Swans switched off almost straight away and from a long ball forward Tony Bennett crossed to an unmarked Nick Kerly to level before half-time.
The visitors took some time to find their rhythm in the second half, but the game opened up as both sides pushed for a winner. Swans brought on fresh legs and that made the telling difference.
Iain Jarvie thought he had scored but his header was ruled out for offside, much to the disgust of the visiting players.
But four minutes before time their luck turned as Luke Jearum’s scuffed shot fell to Robertshaw, who ran on towards goal and slotted past the Oak keeper to steal victory.
Swans boss Nigel Dyer said: “(It was )not the best game to watch as a neutral on a very bumpy pitch which caused both sets of players problems, but the last three games on the road we have taken seven points out of nine, which could easily been all nine if we scored the penalty and did not miss an open goal at Westfield.
“So after a couple of poor results in very tight games against Steyning and Loxwood we seem to got back to playing with a lot of confidence.
“The defence and keeper had another great game with Alex Forsey especially looking like a very decent signing for us. “
Next up is a very tough game When Little Common visit the Recreation Ground next Saturday.
Swans: Chester; Forsey, Setchell, Elliott, Pickford, Watton, Jarvie, Conway, Warner (Robertshaw 65), Humphreys, Rhodie (Jearum 65).