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The Hamlet's stay in the North West started with a fine victory at Chester.
The home side opened the brighter but a solid Dulwich defence made sure that Preston Edwards was not called into serious action. In fact Dulwich went closest when a Christian Smith header came back off the underside of the bar.
Two quick fire goals around the hour put Dulwich in control. Danny Mills scored the first in the 55th minute as he scrambled home the rebound after his volley had been saved.
The second came five minutes later as he seized on the ball after a run from Nyren Clunis and lifted the ball over the keeper.
After a raft of changes, Chester pulled a goal back with a fine effort from the edge of the penalty area by Dudley.
Despite plenty of possession, the home side didn't test Preston Edwards again, whilst Dulwich continued to look threatening on the break through the pace of Dipo Akinyemi and Ade Yusuff.