Resurgent Southwick insist they have still got it all to do, despite a fifth successive win.
A first-half penalty from Daren Newman was enough to see off rivals Peacehaven 1-0 at Old Barn Way in Rich City division two's match of the day.
The result takes Wickers into the promotion places, level on points with Peacehaven, but chairman Peter Keene declared: "We are not counting our chickens yet.
"The great thing is we have beaten three teams who were above us, but we are still looking over at our shoulder at the likes of Oving and Broadbridge Heath."
Hailsham are nine points clear after a 3-0 home win over Bosham. Dean Chamberlain curled home a 25 yard free-kick and scored direct from a corner.
But he was denied a set piece hat-trick when Duncan Jones was pushed in the box.
Jones picked himself up to bury the spot kick.
Boss Mark Leaney said: "Dean wanted the penalty as well but Duncan is our top scorer and it's difficult getting the ball off him.
"We have still got a lot of hard work to do but good results in our next three games will put us in with a great chance."
Broadbridge Heath's recent slump continued with a 3-1 defeat at Shinewater, who are easing away from relegation trouble.
Shine boss Chris Pearce switched to 4-4-2 and admitted: "It was a superb result."
Speedy Graham Holman was moved from a striking role to left back and James Boddy, a recent signing from Eastbourne Town, went up front .
Boddy responded with two goals, including a header from Glen Mitchell's great cross. Wayne Pettigrew was also on target.
Pearce added: "I will probably give the new system a run now.
"We could even finish in the top five or six when we play our games in hand."
East Grinstead retained outside promotion hopes after James Hylton's 12th goal of the season gave them a 1-0 home win over Westfield.
Storrington slipped closer to the drop zone with a 6-2 hammering at Wealden.
Home boss Tom Parker had words of encouragement for Swans. He said: "It was a really open game with lots of chances at both ends but we took a greater proportion of them."
Darren Brown (2), Lee Sale and Tim Brown put Wealden in charge before Simon Rider came off the bench to net twice.
Chris Witten and Ben Whitby replied for Storrington.
Crowborough picked up a handy point by drawing 0-0 at Mile Oak.
Crawley Down also earned a draw, but they felt they could have taken maximum reward after coming from 2-0 down at home to Shoreham.
Andy Agutter and Pat Lawrence struck for the visitors inside 32 minutes after good work by Mark Pulling.
Mike Ducker crossed for his brother Jon to reply with a fierce angled shot and Dave Connor fired the 70th minute equaliser .
Oakwood reached the last eight of the Division Two Cup as a Gerald Manville goal saw off Worthing United. Manville was left unmarked at the far post to head home Zak Newman's cross on 29 minutes.
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