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Welling were left wondering how they came home with nothing to show for their efforts from their Skrill Premier trip to Hereford on Saturday.
The Wings had the best chances, played the better football and limited their opponents but lacked a killer touch in front of goal.
Welling could have been ahead inside five minutes. Rod McDonald was booked for a late challenge on Loick Pires and Jack Obersteller's free-kick had to beaten away at full stretch by keeper Rhys Evans.
Alex Dyer and Ross Lafayette then combined to set up Joe Healy, but he opted for a precise chip rather than power - and his weak effort went straight to Evans.
Lafeyette and skipper Lee Clarke both shot at Evans and Loick Pires shot wide on the turn just before the break.
Hereford had only one long-range shot on target in the opening half but they went ahead on 49 minutes when keeper Lee Butcher fumbled a left-wing cross for Chris Sharp to bundle in.
Pires skipped past left-back Chris Bush but saw his low drive deflected for a corner, Clarke headed over a Doug Bergqvist cross and then Jake Gallagher drove to the byline only to see his low cross go across the face of goal with no-one there to apply the finishing touch.
Welling were made to pay for those misses six minutes from time when Butcher failed to hold a long-range shot and substitute Michael Rankine blasted in from close range, after being played onside by Clarke.
Welling finally scored deep into injury time when Healy's initial header was parried by Evans and his subsequent header was turned in by Lafayette from close range.