The Blues dictated play throughout the opening half but reached the interval empty-handed against an average-looking Cumbrian outfit.
Substitutions were made throughout the second half before Carlisle snatched the contest away from their hosts with two goals in five late second half minutes.
Blues boss Simon Davies emerged from the changing room after the match admitting his defence needed to learn a few lessons from the clash.
Davies was unhappy to see his side failing to take their chances and then having to pay the ultimate price towards the end of the match.
Davies used the match to blood French trialist, Damien Mozika, in midfield, after the player's paperwork had arrived from French League club, AS Nancy.
Mozika proved a real handful for his Carlisle counterparts and demonstrated his ability to spark an attack after breaking up play in the centre of the pitch.
He started the match against Carlisle alongside Tony Dinning, and the impressive former Yeovil Town midfielder, Anthony Barry, who showed a superb first touch and a skill of picking out his marker with long range passes.
But striker Trevor Benjamin, who was due to make an appearance and warmed up on the pitch before the match, was advised to remain on the sidelines because of an eye injury he had sustained.
Chester sprinted out of the blocks and pressurised Carlisle during long spells in the opening half.
Barry released Richie Partridge in the fourth minute who forced a corner after the visitors had struggled to clear the danger.
And Partridge steered a header just wide of the target from a left wing pass by Laurence Wilson as City continued to press for an opening.
John Murphy was unlucky to see his 14th minute headed effort bounce fractionally wide of the post after a superbly worked move initiated by Mozika and assisted by Kevin Roberts.
Barry split the Carlisle defence with an inch-perfect throughball for Partridge in the 17th minute, but the Irishman's effort flew wide.
Kevin Ellison let fly with a 25-yard attempt three minutes later, but his attempt bounced wide of the left post.
And a flowing move combining Mozika, Partridge and Barry, helped set-up Ellison in the 29th minute, but his effort was saved by visiting keeper Chris Howarth.
Carlisle, who seemed content to stand and take everything Chester threw at them, took the lead totally against the run of play in the 36th minute when Tyrone Cameron's long ball provided an invitation for Scott Dobie to run through and smash his 15 yard shot beyond John Danby and into the net.
But City redressed the balance just two minutes later when Ellison won a free kick just outside the visitors' box before dusting himself down and rifling a shot which found the left corner of the net despite a touch off Howarth's hand.
Chester made just one change at the break, left-sided midfielder Ryan Lowe replacing Partridge.
And City picked up from where they left off in the first half with Barry successfully finding his line and length with a spectacular crossfield pass to Roberts who, in turn, centred for Murphy, but his shot was scuffed and comfortably gathered by Howarth.
Mozika tried his luck with a low left-footed 18-yard shot in the 56th minute, but Howarth was alert to the situation.
And Lowe attempted to dissect the Carlisle defence in a bid to pick out Ellison seconds later, but his pass had a touch too much pace and the chance had gone.
Mark Hughes and Stephen Vaughan replaced Dinning and Barry on the hour mark, and Danby had to keep an eye on Danny Carlton's half-volley which fizzed inches over the bar.
On loan striker, Paul Taylor, from Vauxhall Motors, replaced Murphy in the 66th minute as Davies continued to reshape his side, and Paul McManus joined Taylor in the front line when he replaced Wilson.
City finished the game on the back foot as Carlton rifled his 73rd minute shot into the sidenetting; Danny Livesey's 75th minute back post header was cleared off the City line; and Gary Madine's 81st minute header was tipped over the bar by Danby.
But Madine headed home to edge Carlisle into a 2-1 lead in the 82nd minute, and Simon Hackney condemned City to a 3-1 defeat when he profitted from a mix-up between Paul Butler and Danby.
It was disappointing finale for the Blues who had flattered to deceive after providing such a spirited performance.
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