City gained their first point on the road following a hard-fought stalemate against Havant & Waterlooville at Westleigh Park.
Despite both sides' impressive ability to hit the back of the net in midweek, neither team were able to find a way past the gloves of Ross Worner and Carl Pentney.
Both teams registered chances within the first 5 minutes of the afternoon, with Sam Higgins' low struck free-kick being blocked and cleared after being taken out from behind, before Nicky Bailey's set-piece found Jonah Ayunga, who could only direct his header straight into the gloves of Pentney.
Pentney was then called into action again, saving a penalty from Simon Walton. Elliot Omozusi caught Ayunga when attempting to clear his lines, allowing the referee to point to the spot - Walton stepped up, but Pentney guessed correctly before the rebound was headed over the bar.
On an afternoon of many chances, Chelmsford were to threaten next when Higgins found Jamar Loza inside the area. The attacker then got round his marker and managed to force a save from Worner.
Havant cleared their lines only as far as Jonny Giles from the resulting corner, but the midfielders effort from the edge of the area was blocked and cleared away from danger.
Ollie Muldoon was next to threaten from a dead ball situation after Loza was fouled, however his effort hit the wall.
City kept up the pressure though through Chris Whelpdale who managed to get hold of possession and deliver a cross, met by Chez Isaac who couldn't direct his header goal-wards.
Wes Fogden forced another important save from Pentney on the half-hour mark after being played through one-on-one, but the Clarets 'keeper managed to save with his feet, earning a goal-kick in the process.
Alfie Rutherford and Giles then had efforts that hit the woodwork and rose just over the bar respectively, before Havant's Roarie Deacon forced another great save from Pentney just before the break, as he cut in on his left-foot and fired towards Pentney's left.
The Hawks started things off brightly following the interval through Anthony Straker, who provided a dangerous ball into the box towards an un-marked Rutherford, but he just couldn't aim his header towards goal.
Muldoon then struck a free-kick against the wall after Loza was fouled just outside the box, before Havant and Deacon went up the other end, playing a ball through to Josh Taylor who fired an effort just over the bar.
City continued to press for the opening goal despite the hosts pressure, and Higgins very nearly found it with 25 minutes remaining. The Clarets' frontman took aim from the edge of the box before drilling an effort just wide of the target.
Havant then withstood a 5 minute spell of intense pressure from the Clarets. Giles managed to drill and effort just wide of Worner's post, before whipping in a good cross, connecting with Higgins' head which fell narrowly wide.
Isaac was then teed up by Whelpdale, curling the resulting strike just wide.
Havant came close late on as Ayunga skipped past a few challengers and dinked the ball over Pentney only to see his effort go narrowly past the post.
Hawks defender Benny Read then went down inside the area following pressure from Pentney, however the referee saw the Clarets' shot-stopper connect with the ball, before waving away a number of claims for a second penalty of the afternoon.
Second-half substitute, Andy Fennell used his extra energy and pace to pressurize the Hawks defence for the final moments of the afternoon, and was almost rewarded with the winner after taking the ball past Worner but the 'keeper recovered well to block his effort.