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Welling have found goals hard to come by since the departure of striker Adam Coombes to Sutton.
But that did not seem to faze former Dartford and Barnet man Harry Crawford on Tuesday night.
Crawford scored from near the halfway line to hand Welling a 1-0 Kent Reliance Senior Cup quarter-final win over Bromley.
It means the Wings are into the semi-finals where they will host Charlton Athletic.
Dover await the winners in the final, having overcome Folkestone 3-0 in the other semi-final on Monday night at Crabble.