In front of a crowd of 695, the Clarets started well and were rewarded 14 minutes in when, after good work from Chris Dickson and Anthony Church, Bagasan Graham fired home.
Scott Fenwick, who hit the headlines with two successive penalty hat-tricks, was the provider for Chelmsford`s second just before the half-hour mark when he set up Dickson to volley past Stones` keeper Jonathan North.
Half-time saw a change of official due to an injury and then midway through the half saw a bizarre incident when a young ball boy was `dismissed` from the touchline for apparently gesturing to the visiting fans!
But on 68 minutes, just a few minutes after the ball boy had been despatched, City added a third to confirm victory when Dickson cut inside and curled a beauty into the top corner leaving North helpless.
The win leaves City eight points clear of neighbours Braintree Town, who currently occupy eighth spot.