Following conceding ten goals in two games, changes to the back four helped the Wings record a clean sheet.
Matt Fish returned to his right back position following injury and new signings Ben Martin and Phil Walsh made an immediate impression playing their first games together.
Walsh had an early opportunity to make an immediate impression at the other end but was unable to rise high enough to direct goalwards.
After Warren Bentley had failed to find the target when shooting across the face of goal, Luke Williams came closer but Danny Waldren was able to clear at the far post.
Rhys Murrell-Williamson got the better of Rhys Tyler but his volley flew over then Alex Cathline headed wide from a good Fish cross as Welling started to come into the game.
However, Hungerford came back and Chris Lewington blocked out a shot from James Clark before Jordan Brown did well to head away when Nat Jarvis looked favourite to win it.
After the break, Lewington was forced into making a near post save from Bentley before making a brilliant full length one from Matt Day’s free kick.
Pierre Joseph-Dubois replaced Cathline and almost made an immediate impact but headed wide from Murrell-Williamson’s cross.
Walsh then had a header cleared off the line from another Murrell-Williamson delivery as Welling enjoyed a dominant spell.
They thought they had scored when Dan Walker’s shot was blocked out by Lewis Ward straight to the feet of Joseph-Dubois who converted. However, a linesman’s flag meant that it wasn’t to count.
Jon Boardman headed wide for Hungerford but there was still time for Welling to miss one last chance.
Walker’s cross found Joseph-Dubois in space in the area but he was dismayed to miss the target with his header.
Although a win would have eased Welling’s relegation, the point that they won may prove to be crucial at the end of the season.
Welling United: Lewington, Fish, Brown, Fuseini, Martin, Walsh, Walker, Waldren, Cathline (Joseph-Dubois 55), Crawford (Hatton 74), Murrell-Williamson.
Subs not used: Slabber, Agu, Richards.
Hungerford Town: Ward, Tyler, Jones, Boardman, Day, Williams, Clark, Herring, Jarvis (Meechan 73), Bentley, Soares (Goodger 73).
Subs not used: Rees, Thomas, O’Brien.
Welling United:
Goalscorers : None
Yellow cards: Walsh
Red cards: None
Hungerford Town:
Goalscorers: None
Yellow cards: Goodger
Red cards: None
Referee: Gary Parsons
Assistants:.Jack Packman and Shaun Ferrer.
Attendance: 517
Pictures supplied by Dave Budden.
Welling star player: Danny Waldren