Worthing suffered their sixth consecutive defeat when beaten 2-0 at Walton and Hersham in division one.
Barry Lloyd's men have now gone 392 minutes without scoring.
They never really looked like hitting the net against a Surrey side who kept in touch with the promotion pack thanks to a goal in each half from Marcus Rose and James Pearson.
Rebels had to make do without the suspended Danny Smith and Paul Kennett while the midfield lacked bite with Mark Burt out injured.
Paul Rapps, signed from County League division two side Worthing United, had a quiet debut on the right side of midfield and was withdrawn for Gavin Jones 15 minutes from time.
Ben Carrington, who scored Worthing's last goal at Harlow on December 15, set Rapps up for a rare Rebels chance just before the interval that Luke Garrard saved.
By then Rebels had fallen behind with striker Rose converting from six yards after a slip by Mark Knee had allowed Tony Sweet to cross from the right. Pearson wrapped up victory from the penalty spot five minutes from time. Knee was adjudged to have handled a cross from Harkiness as the ball bobbled up after hitting his foot.
Worthing, whose main problem was a lack of support to front runners Carrington and Gavin Geddes, were indebted to keeper James Wastell.
Injury-hit Horsham still had enough strength to beat in-form Chertsey Town 4-0 at Queen Street.
They took the lead in the 16th minute through Lee Carney. Marcel Dennis made it 2-0 in the 25th anms Jamie Taylor scored the third seconds later. Gary Charman made it 4-0 20 minutes from time. They had Tommy Warrilow sent off after 82 minutes.
Three goals in the last six minutes gave Lewes a 4-0 victory against visitors Arlesey Town in a game that had remained even in the previous 84 minutes.
Lewes took the lead on 11 minutes through Marc Cable. Ross Venables doubled the score six minutes from time and Cameron Johnson struck in the 87th and 90th minutes.
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