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Welling suffered their fourth successive Blue Square South defeat after an inept display at home to Eastleigh on Saturday.
In front of a low crowd of 409, the Wings gifted the visitors two first-half goals in one of their worst performances under manager Jamie Day.
The Welling manager did make changes, introducing the likes of Michael Bakare, Jack Obersteller and Luke l'Anson to the starting line-up, but there were few positives to take.
Eastleigh went ahead on 13 minutes when a simple free-kick allowed Richard Gillespie to touch home from close range.
They added a second on 34 minutes, slopping marking allowing Ross Bottomley to head home from close range.
Welling pulled one back with their first effort on target, eight minutes into the second half, when Lee Clarke turned his marker and slotted home.
But the Wings subsequently failed to seriously test keeper Jason Matthews and the visitors held on despite having Tony Taggart sent off for a crude challenge on Graeme Andrews in the last minute.
Bromley suffered a 2-1 defeat at Woking.
Giuseppe Sole put Woking in front with a free-kick from the edge of the box that went in off the underside of the bar after 20 minutes.
Steve Ferguson brought Bromley level five minutes before the break before a goal from substitute Mark Ricketts settled the game.
Colin Luckett’s ninth penalty of the season earned Cray a 1-0 victory over Tooting & Mitcham in the Ryman League Premier Division.