First-half goals from Peter Cooper and Joel Hughes had the home side in control before Hughes struck again and Rikki Cable and Mike McKenna added gloss to the scoreline.
It means nine consecutive defeats for City, who are using the remaining fixtures this season to trial new players amid tough financial times.
Thr bad news is Chichester’s next opponents, Peacehaven & Telscombe, are on a similar run to the one East Grinstead are enjoying.
With six games to go City must be wary of the bottom three in division one of the Sussex League. The Oaklands Park outfit lie 14th and just 12 points clear, with St Francis Rangers in good form and games in hand.
A prime concern for the boss will be in attack, as Chichester have not scored in their past five league games.