Welling hit back to beat in-form Braintree and move to within two points of the Conference Premier play-offs.
The hosts led when Charlie Strutton beat the offside trap to run onto Chez Isaac's pass and fire past Lee Butcher.
Jamie Day's brilliant 25-yard free-kick into the top corner made it 1-1 before the break and Lee Clarke's 12-yard strike put the visitors ahead.
Alex Dyer's driven shot made it 3-1 and Welling held on despite late pressure after Jordan Cox's fine volley.
Town remain in the play-off spots in fifth place.
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