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Welling striker Sahr Kabba scored twice on his first start since returning from a three-game suspension on Saturday.
Kabba came off the bench in midweek against Chester but he marked his return with a first-half brace as Loui Fazakerley's Welling made it three wins in a week in the National League.
A largely dull first half came to life in two minutes before half-time.
Halifax keeper Matt Glennon somehow fumbled Sam Corne's header from Ben Jefford's left-wing cross and Kabba pounced from close range to put Welling ahead.
The lead was doubled two minutes later when Ricky Wellard crossed from the right-wing and Kabba, after his initial shot was blocked, fired in with his left foot to make it 2-0.
Prior to that, the best chances of the half had gone to Halifax, But James Bolton headed over and then the same player shot weakly at keeper Tom King.
Halifax had the ball in the net five minutes before half-time but Hamza Bencherif's follow-up after King spilled a long-range shot was ruled out for offside.
At the other end, Wellard twice went close while George Porter saw an early effort tipped over by Glennon.
In the second half, Halifax continued to create half-chances but they couldn't find a way beyond King.
Porter and Wellard continued to impress at the other end for Welling but Porter's wait for a Welling goal continued after Glennon somehow kept out his header.
Jefford made an excellent driving run forward and exchanged passes with Wellard before failing to produce a finish to match.
Just minutes after Halifax's Sean Tuton was booked for a dive in the penalty area, Welling had an appeal of their own turned down. Kabba failed to force the ball in for his hat-trick and Wellard's follow-up was blocked by what appeared to be an outstretched arm.
Welling started to dominate in the final stages. Porter weaved his way into the box but was denied at the near post before Wellard's rebound was blocked by the feet of Glennon.
Porter was hauled down late on by Julian Banton but no free-kick was forthcoming before Wellard shot over with what proved to be the last telling action of the afternoon.
Welling have now won three games on the bounce in the National League and are five points clear of the drop zone.
Welling: King, Jefford, Chambers, Porter, Lee, Kabba (Awotwi 80mins), Wellard, Nortey, Lokko, Corne, Vidal. Subs not used: McEntegart, Osborne, Adeyinka, Obafemi.
FC Halifax: Glennon, Bolton, McManus (Hattersley 88mins), James, Bencherif, Burrow, Walker (Hibbs 72mins), Brown, Roberts (MacDonald 67mins), Tuton, Banton. Subs not used: Porter, Racchi.
Attendance: 653.