Billingshurst manager Mark Betts was left pinching himself in hope the failure of his dominant side to take a least a point on Saturday was all a bad dream.
Ben Brooker fired the hosts ahead on 20 minutes with one of his hardest chances of the afternoon, before former Hurst man Marcus Strevens equalised eight minutes later.
A back-heeled effort from Oli Leslie was then cleared off the line and hit Nathan Stepney and flew into the net.
Wickers levelled again through a bizarre own-goal before the break as Dean Smith smacked into the ball 25 yards out and it hit Dan Stepney and looped over a stranded Tom Betts into the top corner.
Billingshurst dominated the second-half but disaster struck with ten minutes left as Tom Donnelly pinched an undeserved winner.
Mark Betts said: “It was frustrating because we had enough chances to win by a country mile. Wayward finishing and bad decisions let us down in the end.
“I cannot understand how we have come away with nothing – you have to pinch yourself when after you realise that.
“It’s a results business, but the result says Southwick three and Billingshurst two and it’s a head slap moment when you did not get something, yet alone all three points.
“We totally dominated possession and the stats would have shown we had 32 shots on target to probably four – there tells the story.”
Billingshurst: Betts, Taylor, Lambkin, Sleat, D.Stepney (R.Carse 60), N.Stepney, Chadwick, Gravestock (J.Carse 70), Tilley, Brooker, Leslie.