On an afternoon which saw title contenders Torquay United and Woking both come out victorious in their respective matches, City ended the day ten points adrift of the summit and slipped into fourth place.
Stefan Ljubicic put the hosts ahead on four minutes with a tidy finish past Nathan McDonald after capitalising on poor defending from the Clarets. Rhys Murphy restored parity midway through the second half by poking the ball over the line from close range.
City boss Rod Stringer made just one change from the side that drew 2-2 with Concord Rangers last weekend; Max Porter replaced Anthony Church alongside Chez Isaac in midfield.
Chelmsford were keen to end a run of two consecutive draws by beating Boro’ but Stringer’s side were dealt a blow as they fell behind inside the opening five minutes. City failed to clear their lines in a wide position and, after a low ball was delivered into the box, Ljubicic made no mistake by sweeping a shot into the top corner.
In a fairly end-to-end encounter, both sides threaten to score shortly after the game’s opening goal. Murphy could only muster a tame effort when he bore down on Mark Smith’s goal, Ljubicic then had a deflected effort trickle through to McDonald.
The Clarets should have levelled on twelve minutes but were left frustrated once more. Scott Fenwick controlled well inside the Eastbourne half and sent Murphy into space; however, the City top-scorer had a weak shot dealt with comfortably by Smith.
Ryan Hall’s audacious shot from range almost snuck past McDonald at the near-post, but the City shot-stopper made a low save to turn the attempt round the post.
Chris Whelpdale’s teasing cross met a powerful header from Fenwick inside the six-yard box, but the striker glanced his header wide as City entered the break a goal behind.
With the blustery wind now in their assistance, City dominated the majority of the second half.
Murphy squeezed into space on 52 minutes, dinking past numerous defenders before pulling the ball back to Jonny Giles, but the final attempt was saved well by Smith at close-range.
City boss Rod Stringer opted for a double change on the hour-mark as he looked for a way back into the tie; Fenwick and Chris Gregan came off as Jordan Chiedozie and Tom Wraight entered the action and the substitutes had an immediate impact.
The two substitutes linked up well on the left to win a corner. Giles delivered the set-piece into the box and, after a few seconds of pin-ball, Murphy reacted quickest to a loose ball to fire home from close range to level the fixture.
Chelmsford’s poor defending almost allowed Josh Bingham to restore Eastbourne’s leader after beating the offside trap, but Adrian Cascaval recovered to deny the striker with an excellent sliding tackle.
The hosts were lucky to escape being reduced to ten-men with fifteen minutes still to play. Kristian Campbell received a yellow card for kicking the ball away and, moments later, the left-back was fortunate not to receive his marching orders after brutally fouling Giles.
City came close from the subsequent free-kick, but Porter’s long-range effort was tipped over the bar. Isaac curled the following set-piece towards Michael Spillane, but the defender was unable to keep his effort on-target as it deflected over the bar.
Stringer made his final change five minutes before full-time, replacing Giles with Aaron Cosgrave as the Clarets looked to convert their dominance into a goal.
The late substitute almost provided that late winner as he twisted and turned past several defenders before bending a shot towards goal; however, it curled narrowly over the bar.
Eastbourne Borough had their own chances to salvage all three points when Hall and Bingham came close to netting, but City held on for what could be an important point at the end of the season and to extend their unbeaten run in the League to nine games.