Burgess Hill's poor start to the campaign seems a distant memory after victory at Dulwich.
Hillians' fifth league win keeps them second, six points behind Wimbledon who have a 100 per cent record after seven games.
Steve Harper put them in front after Matt Geard's cross was handled and Geard got another assist when his cross was headed home by Tom Edmonds.
Hamlet rallied in the second half and former Crawley midfielder Peter Garland halved the deficit with a 67th-minute penalty, but the visitors held on.
Assistant manager Darin Kilpartrick said: "After going out of the FA Cup last week it was a fantastic result. We dictated the play for long periods and created some good chances."
Meanwhile, Hastings moved third after Carl Rook's goal proved decisive against Bromley at the Pilot Field.
Rook got on the end of Russell Eldridge's 32nd-minute free-kick after Bromley had dominated early on.
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