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Welling’s long wait for a goal continued after they were held by Dulwich on Tuesday night.
It’s now 461 minutes since the goalshy Wings last scored in National League South - and they’ve taken just two points from their last five matches.
Welling started brightly enough with keeper Charlie Grainger having to save Nathan Green’s left-foot shot before pouncing on the rebound.
Willing lone striker Korrey Henry got his feet muddled up after some promising approach work and could only win a corner before the forward set up Montel Agyemang, who curled his shot wide of the upright from 25 yards.
Sanchez Ming was allowed time and space to advance down the right before Grainger did well to keep out his 20-yard drive at full stretch.
Dulwich, possibly still trying to get Friday’s FA Cup exit out of their system, offered little as Welling captain Rob Swaine kept former Wings striker Danny Mills largely in check.
The chances fell to Welling again after the break, Cook’s free-kick was well saved before the same player’s header was comfortably kept out by the safe hands of Grainger.
Green drove forward, with Dulwich backing off, and went inches away from finding the top corner when he took the shot on.
Dulwich made a double change midway through the half, taking off the ineffective Ade Yusuff and Jeffrey Monakana.
They nearly found a breakthrough moments later but substitute Lewis White fluffed his lines from close range.
Swaine produced an excellent recovery block to deny White with 16 minutes left after Dominic Vose’s precise through ball sent him behind the Wings defence.
Swaine nearly ruined a decent night's work when he sold keeper Dan Wilks horribly short with a backpass but Wilks did brilliantly to thwart Dulwich's Nyren Clunis.
Agyemang nearly found the top corner with another effort from distance but Welling had to withstand some late Dulwich pressure with White wasting another golden chance while Mills had a header diverted over the bar.
Welling: Wilks, Ming, Anderson, Agyemang, Swaine, Okosieme, Cosgrave (Widdrington 81mins), Waldren, Henry, Cook, Green. Subs not used: Rich-Baghuelou, Anau, Rooney.
Dulwich: Grainger, McCoy, Smith, Dempsey, Orlu, Smith, Chapman, Vose, Mills, Yusuff (Clunis 68mins), Monakana (White 68mins). Subs not used: Connors, Ijaha, Barnes.
Attendance: 469.