Welling backed up their midweek point with a battling three points in horrendous weather conditions at Dulwich Hamlet on Saturday.
Anthony Cook saw a free kick saved early on by Charlie Grainger, Harold Joseph firing the rebound wide.
Just eight minutes had passed when Welling scored what turned out to be the winner. Cook produced a good free kick into the area which came to Romoney Crichlow-Noble he saw his initial effort blocked, but the rebound fell nicely for him and he fired home much to the delight of the large travelling Wings fans.
Ben Chapman shot from range with Wilks making a fine save.
Nyren Clunis had an audacious overhead kick go wide.
Cook fired over after good-work between Dipo Akinyemi and Cameron James has set them up.
Goldberg then pulled the ball back but again Cook failed to hit the target and side footed over.
David Ijaha curled well wide for the home side as they tried to get back into the game.
Dan Wilks then produced the save of the game Quade Taylor’s downward header looked to be heading in only for Wilks to somehow push it away drawing applause from all four sides of the ground. The Wings keeper was at it again pushing around a shot from Nyren Clunis.
Clunis fired well wide early in the second half before Welling lost influential defender Crichlow-Noble to a nasty looking injury. The Huddersfield loanee was hit by a trailing elbow catching him on the cheekbone and he had to be replaced by Connor Dymond.
Nathan Green saw a low free kick saved.
Grainger had to be alert to save well from Goldberg’s twenty yard shot before Wilks had to be on fine form once again to push away Clunis header.
Former Welling man Danny Mills shot wide from range but it was Welling who should have doubled their lead. Diaz Wright played a lovely one-two with James but with just Grainger Wright fired over.
Wilks capped a fine display with the clean sheet he deserved as he managed to push a wind assisted effort from Jack Connors over the bar.
Welling now look ahead to two Saturday home games starting with Chippenham Town this coming weekend.
Welling United: Wilks, Johnson, Green, Joseph, Crichlow-Noble (Dymond 51), Wright, James, Goldberg (Rolt 77), Akinyemi, Roberts (Agyemang 88), Cook. Subs not used: Coombes, Henry.