Following defeat at Torquay United, Jamie Day made two changes to the Welling line up, Zach Fagan and Barney Williams replacing Rod Young and the injured Ben Jefford.
FC Halifax Town's Lois Maynard had a header cleared at the near post by Loui Fazakerley as Welling started to come to terms with a different system.
Steve Williams then saw a header from Marc Roberts' long throw hit the outside of the post.
An injury to Joe Healy did not help Welling's cause an while he was receiving treatment off the pitch, Scott Boden had a looping header tipped over by Lee Butcher. Healy was unable to return and was replaced by Charlie Gorman.
Matt Glennon did well to clear a swirling Harry Beautyman free kick after a bad foul by Williams on Tyrone Marsh.
Maynard hit a shot just wide of the post before Fagan made a crucial header away from an enticing cross.
Another Roberts long throw caused chaos and Maynard headed just beyond the far post as Welling struggled to contain the direct tactics employed by the hosts.
Adam Smith found Boden shortly before the break but his shot was deflected just wide for a corner.
Harry Beautyman recorded a goal attempt for Welling just beyond the break but launched his effort well over.
FC Halifax made a double substitution at the break, bringing on Jamie Jackson and Richard Peniket and it paid dividends immediately.
The endeavour of Jackson won the hosts a corner that Paul Marshall delivered for Roberts to rise and head home.
Four minutes later Peniket made it two thanks to an unselfish pass by Boden.
Marsh had a chance for Welling but Glennon got down well to push out with nobody following up.
Good skills by Marsh almost played in Afolabi Obafemi, but it got away from him and a foul on the goalkeeper ended the danger.
A good advantage gave Maynard another shooting chance but again, he was just off target.
Chris Bush broke out well and exchanged passes with Marsh, before the Oxford United loanee shot wide.
Things went from bad to worse after 76 minutes when another Marshall corner was headed back by Williams for Peniket to smash into the roof of the net.
It could have been four when Scott McManus sent Jackson away but his chipped cross shot clipped the bar.
Yet another Marshall corner wasn't defended and Roberts' free header was cleared off the line by Gorman.
There never looked likely to be any comeback for the Wings as Halifax cruised to victory.
Welling United: Butcher, Fazakerley (Young 85), Williams, Fagan, Bush, Fyfield, Beautyman, Gallagher, Abofemi, Marsh, Healy (Gorman 10). Unused substitutes: Turner, Corne, Day.