It took the Clarets just eight minutes to open the scoring when Billy Bricknell's effort was deflected in off a Heybridge defender before Anthony Church - one of 14 new signings made by Rod Stringer since joining the club - made it 2-0 just before the half time interval.
Stringer made 10 changes to his side for the second half, with the goalkeeper the only one surviving, and City blitzed through a young Heybridge side with three goals in five second half minutes.
The first came from a trialist who rose highest to head the ball in from a corner right on the hour mark, before Hugo Skepelhorn was brought down in the area four minutes later with the referee awarding a penalty which Jake Reid converted.
Less than a minute later and Luke Daley found himself in the area and he rounded off the scoring with a delicately placed chip over the advancing goalkeeper to make it 5-0.
The hosts did manage to grab a consolation goal with four minutes remaining as their striker beat the offside trap to be through one on one, finishing cooly.
The Clarets now move forward to their next pre-season game against St. Neots Town next Tuesday.