Swans started the game brightly and went ahead after just eight minutes when Kristian Harding beat the offside trap and slotted home his seventh goal of the season.
Harding then missed an opportunity to double his side’s lead when he shot wide from just five yards and Wick levelled on 29 minutes.
A misunderstanding in defence between Tom Pickford and Ian Jarvie saw them both jump for the ball, which fell kindly for Callum Cutler, who went through one-on-one and fired home.
Craig Grantham and Harding had opportunities to restore Storrington’s lead before half-time, but it was Wick who went ahead on 52 minutes.
Pacy winger Michael Asare broke into the penalty area and, with Swans backing off, he shot home.
Storrington tried to get back into the game, with Grantham and Harding going close, but Wick held on to all three points.
Swans joint manager Nigel Dyer said: “It was a fairly decent game and, in the first half, we were the better side and probably should have gone in two or three ahead at half-time.
“The second half was a lot more even and there was not much between the two teams.
“If we’d gone 2-0 ahead, I think their heads would have dropped and it could have been a similar scenario to when we beat Westfield 4-0 last week.
“We were disappointed not to be ahead at half-time and we should have stopped Asare before he got their winner. He’s so quick, like Usain Bolt, and he got into our area after a mazy run but we should have got a block or a tackle in.”
Swans travel to Seaford on Saturday and have defender Sam Elliott back available after suspension, but midfielder Richard Maymon still has two games of his three-match ban to serve.
STORRINGTON: G.Elliott; Dixon, Pickford, Carter, Rhodie; Humphreys, Jearum, Jarvie; Grantham, Harding, Measom. Subs: McLeod, Davis, Miles (Jearum, Rhodie, Harding 70).