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Charlie Penny scored his second goal in as many games to move Welling up to 18th in Vanarama Conference on Tuesday night.
The Wings completed the double over Braintree with a deserved victory at Cressing Road thanks to Penny's close-range finish just after the hour mark.
The victory came just 24 hours after Welling sold leading scorer Harry Beautyman to League 1 outfit Peterborough.
Without the suspended Jamal Fyfield and Chris Bush and with Ben Jefford and Loui Fazakerley both injured, Welling fielded a young back four with on-loan Crystal Palace defender Michael Chambers the oldest at 20 and development squad teenager Joey Taylor making his first league start at left-back.
Chances were few and far between in the first half, although Welling twice went close from Jamie Day corners with headers from Zac Fagan.
The Wings started to get on top early in the second half and Penny fired them ahead. It was a lead they never looked like losing as Braintree rarely called keeper Benji Buchel into action.
The hosts were then fortunate to avoid having a player sent-off late on when Penny was fouled after he appeared to be clean through on goal.
Welling travel to Bristol Rovers this Saturday before, in an unusual run of fixtures, hosting the same opposition at Park View Road seven days later.