Welling suffered a setback when defender Paul Copley was injured warming up for Saturday's 2-2 draw with Morecambe.
Wings took the lead on nine minutes when Mark Cooper's shot came off a defender and was fired home by Ritchie Hanlon.
Welling went further ahead on 23 minutes when Hanlon spotted Mark Hynes and delivered a through ball for the striker to coolly past keeper McLharghey.
In the second half, Terry Skiverton was booked for what looked a challenge on the edge of the box. Healy, for the vistors, looped the resulting free kick over the wall and wide of Wings keeper Glen Knight. Morecambe levelled on the hour.
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