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Welling remain rooted in the Vanarama National League South relegation zone after another defeat on Saturday.
The Wings were dumped out of the FA Cup by Whitehawk last weekend and lost to the same opponents again at Park View Road.
This time Welling did put up more of a fight in the first half but they lacked fitness in the second half and ran out of steam.
Welling handed Christian Nanetti a debut in their forward line. His tireless work and clever movement never gave the Whitehawk defence a moment's peace all afternoon.
Nanetti created a chance in the 16th minute but never got his shot away when he had time and space to shoot and the chance was gone.
Whitehawk went ahead against the run of play on 20 minutes. Welling's Craig Braham-Barrett failed to clear his lines and Rickie Hayles' challenge on Danny Mills was penalised with a penalty.
Ahmed Abdulla's spot-kick to Chris Lewington's left was saved by the Wings keeper but Abdulla followed up to convert the rebound.
Welling's response was immediate as they levelled within two minutes. Nanetti's cross perfectly picked out Adam Coombes, who headed in his 13th goal of the campaign.
The Wings continued to dominate possession and territory but chances were hard to come by. Danny Waldren headed over from a corner before his low shot was saved by keeper Ross Flitney.
Whitehawk enjoyed their best spell at the start of the second half. Mills failed to hit the target after another Braham-Barrett error before Mike West's shot was deflected wide for a corner.
The visitors continued to dominate and their pressure was almost rewarded on 65 minutes when Ben Strevens' free-kick was deflected narrowly wide for a corner.
Welling had two late openings as Sam Hatton turned wide a near-post Nanetti cross before the latter's speculative 20-yarder.
Welling: Lewington, Fish, Braham-Barrett, Fuseini, Francis, Hayles, Hatton, Waldren, Nanetti (Johnson 89mins), Coombes, Della-Verde. Subs not used: Leacock, Agu, Nelson. Attendance: 447.