Haysman stooped low to head home on nine minutes after Chris Dickson did superbly to produce a cross from a tight angle.
Theophanous put City further in the ascendancy when his driven effort sneaked through Sam Howes after Robbie Willmott provided the assist for the City striker.
Chelmsford withstood an early attempted raid from the hosts with excellent style as the defence stood unbroken and resolute.
And Rod Stringers’ side’s early strength eventually displayed a reward when the Clarets broke on the attack. Willmott sprayed the ball to Dickson who, from an acute angle, managed to drive the ball across goal to Haysman who fought his way through a crowded box to head in at the far post.
A strong away contingency of supporters aided the visitors when nerves began to show when City skipper Anthony Church shanked a clearance, however it lacked any difficulty as it bobbled back to Ross Fitzsimons.
Theophanous almost doubled his side’s lead when he latched onto Josh Rees’ inch-perfect through ball, however the Greek striker was denied a goal by a superb save from Howe.
The Clarets got themselves in a muddle again when Josh Hill and Michael Spillane came together for a long ball forward, but Fitzsimons was on-par again to gather the loose ball.
Theophanous eventually got his reward for arduous work as his driven shot snuck into the bottom corner at the far post on the half hour mark.
The lead was almost increased to three late in the second half, however Theophanous was unable to keep his shot low after Dickson had done so well to juggle the ball.
Hampton failed to make any impact from their first chance of the half, as Brendan Kiernan rifled into the side netting from distance.
Chances came at a cost in the second half, with Anthony Church and Josh Rees both coming close for the Clarets. However a resolute defence made sure that a consolation was not conceded, and that three vital points would be heading back to Essex.
Chelmsford: Fitzsimons, Hill, Spillane, Miller, Willmott, Daley, Church, Rees, Haysman (80 Buchanan), Dickson (70 Jeffers), Theophanous (88 Cornhill). Unused Subs: Porter, Blanchett.
Goals: Haysman 9, Theophanous 30.
MoM: Josh Rees