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Andy Pugh's second goal in as many games saw Welling claim their first Blue Square Bet South win on Wednesday.
The Wings scored at the end of each half with Lee Clarke scoring just before half-time.
Welling player/boss Jamie Day was ruled out by injury so Loick Pires joined a three-man forward line.
Luis Cumbers went close for Welling in the first half while, at the other end, the lively Craig Braham-Barrett caused the visitors plenty of problems.
Former Welling full-back Braham-Barrett, who was sold to Peterborough for £10,000 in October 2008, tested Loui Fazakerley to the full as he impressed against his former club.
Welling took the lead just before half-time, however, when Luis Cumbers was fouled by keeper Nathan Ashmore. The Havant man escaped a red card but his luck ran out when he saved Clarke's spot-kick only for the Wings midfielder to convert the rebound and put his team ahead.
Welling's lead lasted less than a minute as Braham-Barrett's low shot was saved by keeper John Whitehouse but the assistant referee signalled that it had crossed the line.
After the break, the impressive Cumbers again went close for Welling but it was Havant who should have gone ahead when Braham-Barrett was fouled in the area, only for Mark Nwojeki to blaze his spot-kick over the bar.
Welling claimed the winner with eight minutes left when a dangerous Fazakerley free-kick was glanced in at the near post by Pugh (pictured).
The home side were reduced to 10 men late on when Steven Ramsey was shown a second yellow card.
Havant is fast becoming a happy hunting ground for the Wings, who are now unbeaten in their last three visits to Westleigh Park.