Michael Ademiluyi scored the only goal on 20 minutes, curling the ball beyond an unsighted Kieran Magee to give the hosts three precious points in their bid to beat the drop.
Etienne Frimpong was given a debut for Chi at left back in an otherwise unchanged starting XI from the one that thumped fourth-place Whitehawk 4-1 midweek at Oaklands Park.
Faversham started on the front-foot and City skipper Connor Cody had a cross to block 60 seconds in.
A home side throw-in then caused some problems as the visitors conceded the first corner of the match which Matt Parsons whipped over only for the back four to clear their lines.
Frazer Shaw and Ademiluyi linked up but Isaac Bello headed away before Cody steered the ball out for a second corner in as many minutes that Callum Overton got clear.
Under pressure, Chi had a dangerous delivery to contend with, although Shola Ayoola had strayed offside.
And then against the run of play Lloyd Rowlatt fed Kaleem Haitham after Overton flicked on and leading marksman Ethan Prichard couldn’t tuck home a measured cross from the right.
Next, Rowlatt’s neat turn and pass set Prichard up for another attempt which nicked off a defender for a corner that Rowlatt took and Emmett Dunn got a connection on of sorts.
Keeper Magee was forced into a super save by Parsons in the ninth minute as Faversham pressed once more.
A lovely cross-field ping helped the away team counter only for the move to fizzle out.
And then a heavy challenge from Frimpong on Ademiluyi driving into the penalty area gave referee Howard Collins a decision to make – no pen.
Ayoola won a corner off Frimpong moments later that Parson played short to Kieron Campbell and Dunn cleared.
Campbell and Ayoola threatened again but Bellow hooked the ball out for a throw-in.
Magee was off his line swiftly ahead of Ronald Sithole before Ademiluyi broke the deadlock with a strike which nestled in the bottom left hand corner.
The Chi custodian then overplayed on the edge of his 18-yard box and might have been outdone by Ayoola but got away with one.
Haitham did Ademiluyi just before the half hour mark, and cut inside, only for Bailey Vose to gather easily enough.
Bode Anigdube sent Sithole away on a chase but Cody tidied up and an outstanding tackle by Harrison Byford on Overton at the other end prevented the Chi striker from getting to a lofted forward pass.
Ademiluyi picked Frimpong’s pocket only to play a poor ball in before Bello’s long throw into the area was smuggled out to Rowlatt whose rocket deflected off a defender and over.
Rowlatt’s subsequent corner popped about in the penalty area and was finally hooked out for another throw which Bello launched and the hosts directed for a corner.
Vose got a glove on this one and the Kent side countered with Ayoola being denied by an upright.
Momentum shifted this way and that as Rowlatt almost picked Overton; both Haitham and Prichard couldn’t quite get the loose ball under control after Bello’s throw was hacked away; and Faversham CB Olly Gray outfoxed Overton and headed back safely to Vose.
The hosts dug in protecting their slender lead.
Prichard forced Vase to spill his effort but claim at the second attempt, and another couple of moves came to an end for Chi as final passes went astray on the stroke of half time.
Joe Clarke sent Haitham scampering away down the left in the first attack of the second 45 for a misplaced cross and then was well-up but Haitham lost the ball this time.
Campbell broke along the flank and pulled a decent stop out of Magee.
And Magee’s crossbar came to his aid four minutes in when Sithole’s hell of a screamer somehow cannoned back off the woodwork.
Another hit struck Bello and went out for a corner which Anodugbe disappointingly swung into the side-netting.
Byford then took the ball skilfully on his chest and moved it on to Ademiluyi whose cross was cleared.
Haitham and Clarke made way for Olly Munt and Josh Clack on 53 before Ryan Davidson and Ayoola duelled for a ball which Davidson won, taking a knock for his trouble in the process.
On the hour Ayoola spurned a glorious opportunity to double the hosts’ advantage cracking one into the advertising boards rather than the back of the net when it seemed easier to score.
Three corners came and went in quick succession for Chichester without any profit as Faversham continued to defend resolutely.
Magee had to have his wits about him as first Ayoola and then Sithole caused trouble.
Frimpong was withdrawn for Joe Moore with 20 to go and then Parsons got in down the left and Campbell drilled an effort over the bar.
Dunn defended superbly to deny Sithole before Rowlatt played an inviting ball through to Overton who wasn’t able to get a firm connection.
An accurate pass from Parsons for Sithole teed up another chance for the home side.
And then Chi blew opportunities of their own late on as Prichard took a touch too much, Dunn had a shot blocked, and Clack headed Prichard’s cross off target.
Next, the visitors conceded two needless corners, one of which presented Byford with a free-header, and in the last minute of the six added on Sithole fluffed his lines.
So, the unbeaten sequence, in which Chichester scored 21 goals and kept five clean sheets, is over.
This hasn’t been a happy hunting ground for Chi the past few seasons – three losses in three now.
Faversham, who are into their third management team this season and have churned over a raft of players looking for that great escape, leapfrogged Corinthian at the foot of the table as a consequence of the win.
Miles Rutherford’s men return to Kent on Tuesday 7th March against Sittingbourne (Kick Off 7:45pm) and Saturday 11th March to face Hythe Town (Kick Off 3pm).
Chichester – Magee, Bello, Frimpong, Clarke, Cody, Davidson, Haitham, Dunn, Overton, Rowlatt, Prichard (Weinberger, Clack, Moore, Munt, Pashley).