Erkan Oztumer and Connor French struck early in the second half to make it 3-0 and, after Tony Nwachukwu pulled one back with a penalty, current Liverpool trialist Danny Carr completed the scoring.
Dulwich moved to within three points of table-topping Maidstone with a game in hand, while Horsham remained just three points above bottom club Three Bridges and have now played only two matches fewer.
Whitstable eased their own relegation fears with a 1-0 home won over Merstham. Oliver Lee scored after 18 minutes, lifting the Oystermen two places to 17th.
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