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Welling were left looking nervously towards the Vanarama Conference relegation zone after losing at home to fellow strugglers Alfreton on Saturday.
Two late goals failed to paper over the cracks of an awful defensive display from the Wings and means new boss Jody Brown is still waiting for his first win in charge.
The Wings trailed 2-0 at half-time to two Bradley Wood penalties. Jamal Fyfield was beaten for pace before he hauled down John Johnston in the ninth minute and Wood found the bottom corner from the spot.
Veteran defender Darren Purse conceded the second spot-kick five minutes before the break and Wood put his penalty in exactly the same place.
In between, Alfreton barely had an attack worthy of the name while Welling had plenty of possession but little cutting edge. The offside flag thwarted Charlie Penny on three occasions while debutant Dominic Vose was the pick of the Welling attack, probing and running with the ball intelligently while going close with a long-range shot.
After the break Welling introduced Ronan Vine from the bench but they had only a deflected Jake Gallagher shot to show for their efforts by the time Alfreton made it 3-0 on 74 minutes when Karl Hawley scored at the second attempt after Welling failed to cleared their lines following Jonathan Henly's impressive initial save.
Vose was fouled by Luke Graham and Vine tucked away the third penalty of the game with three minutes left to make it 3-1.
Substitute Malachi Hudson was denied a stunning goal when keeper Jason Mooney tipped over his left-foot shot in the 89th minute - and it proved a crucial save as Chris Bush headed in when Vine nodded across Fyfield's free-kick in the fourth minute of stoppage-time.